In order to better describe the phenomenon of biological invasion,this paper introduces a free boundary model of biological invasion.Firstly,the right free boundary is added to the equation with logistic terms.Secondl...In order to better describe the phenomenon of biological invasion,this paper introduces a free boundary model of biological invasion.Firstly,the right free boundary is added to the equation with logistic terms.Secondly,the existence and uniqueness of local solutions are proved by the Sobolev embedding theorem and the comparison principle.Finally,according to the relevant research data and contents of red fire ants,the diffusion area and nest number of red fire ants were simulated without external disturbance.This paper mainly simulates the early diffusion process of red fire ants.In the early diffusion stage,red fire ants grow slowly and then spread over a large area after reaching a certain number.展开更多
This paper studies certain estimates for the lower bound of distance between unitary orbits of normal elements.We show that the distance between unitary orbits of normal elements of simple C^(*)-algebras of tracial ra...This paper studies certain estimates for the lower bound of distance between unitary orbits of normal elements.We show that the distance between unitary orbits of normal elements of simple C^(*)-algebras of tracial rank no more than k has a lower bound.Furthermore,if k≤1 and normal elements are commuting,then the lower bound will be better.Another result establishes a connection involving the spectrum distance operator Dc between a C^(*)-algebra of stable rank one C^(*)-algebra and its hereditary C^(*)-subalgebra.展开更多
The weakly compressible smooth particle hydrodynamics(WCSPH)model is studied to address the boundary pressure instability of the SPH method,resulting in the development of the SPH method with improved dynamic boundary...The weakly compressible smooth particle hydrodynamics(WCSPH)model is studied to address the boundary pressure instability of the SPH method,resulting in the development of the SPH method with improved dynamic boundary conditions.This method employs the‘fan’search method for free surface detection,effectively identifying cavity interface particles with diameters smaller than the support domain’s radius,thereby indirectly enhancing the algorithm’s accuracy.On this basis,an improved dynamic boundary condition is proposed by updating the boundary particle pressure calculation scheme to achieve a more stable and continuous pressure field,thereby effectively preventing particles from penetrating the boundary.The SPH method with improved dynamic boundary conditions is used to simulate typical high-speed impact problems such as wedge entry and dam break.The simulation results are in good agreement with the experimental data and other numerical results.展开更多
In this article,we show the existence,uniqueness and stability of bounded solutions to the following quasilinear problems with mean curvature operator(φ'(x′(t)))′=f(t,x),t≥t_(0),lim_(t→∞)x(t)=ψ_(0),lim_(t→...In this article,we show the existence,uniqueness and stability of bounded solutions to the following quasilinear problems with mean curvature operator(φ'(x′(t)))′=f(t,x),t≥t_(0),lim_(t→∞)x(t)=ψ_(0),lim_(t→∞)x′(t)e^(t)=0,where t_(0) and ψ_(0) are real constants,φ(s)=s/√1−s^(2),s∈R with s∈(−1,1),f:[t_(0),∞)×R→R satisfies the Lipschitz or Osgood-type conditions.展开更多
Alkali-free SiO_(2)-Al_(2)O_(3)-CaO-MgO with different SiO_(2)/Al_(2)O_(3)mass ratios was prepared by conventional melt quenching method.The glass network structure,thermodynamic properties and elastic modulus changes...Alkali-free SiO_(2)-Al_(2)O_(3)-CaO-MgO with different SiO_(2)/Al_(2)O_(3)mass ratios was prepared by conventional melt quenching method.The glass network structure,thermodynamic properties and elastic modulus changes with SiO_(2)and Al_(2)O_(3)ratios were investigated using various techniques.It is found that when SiO_(2)is replaced by Al_(2)O_(3),the Q^(4) to Q^(3) transition of silicon-oxygen network decreases while the aluminum-oxygen network increases,which result in the transformation of Si-O-Si bonds to Si-O-Al bonds and an increase in glass network connectivity even though the intermolecular bond strength decreases.The glass transition temperature(T_(g))increases continuously,while the thermal expansion coefficient increases and high-temperature viscosity first decreases and then increases.Meanwhile,the elastic modulus values increase from 93 to 102 GPa.This indicates that the elastic modulus is mainly affected by packing factor and dissociation energy,and elements with higher packing factors and dissociation energies supplant those with lower values,resulting in increased rigidity within the glass.展开更多
This study examines the effects of friction stir welding(FSW)and post-weld heat treatment(PWHT)on the grain boundary character distribution and corrosion resistance of cross sectional(top and bottom)regions of nickel-...This study examines the effects of friction stir welding(FSW)and post-weld heat treatment(PWHT)on the grain boundary character distribution and corrosion resistance of cross sectional(top and bottom)regions of nickel-and molybdenum-free high-nitrogen austenitic stainless steel(HNASS).FSW at 400 rpm and 30 mm/min resulted in finer grains(4.18μm)and higher coincident site lattice(CSL)boundaries(32.3%)at the top of the stir zone(SZ)due to dynamic recrystallization(DRX).PWHT at 900℃for 1 h led to grain coarsening(12.91μm the bottom SZ)but enhanced CSL boundaries from 24.6%to 30.2%,improving grain boundary stability.PWHT reduced the kernel average misorientation(KAM)by 14.9%in the SZ-top layer and 20.4%in the SZ-bottom layer,accompanied by a 25%decrease in hardness in the SZ-top layer and 26.7%in the SZ-bottom layer,indicating strain recovery and reduced dislocation density.Potentiodynamic polarization tests(PDP)showed a 18%increase in pitting potential and a 76%reduction in corrosion rate after PWHT.The improvement in corrosion resistance is attributed to the increase inΣ3 twin boundaries,which enhance grain boundary stability and reduce susceptibility to localized corrosion.These findings highlight the role of PWHT in refining the microstructure and strengthening corrosion resistance,making HNASS a promising material for demanding applications.展开更多
Understanding the complex plasma dynamics in ultra-intense relativistic laser-solid interactions is of fundamental importance for applications of laser-plasma-based particle accelerators,the creation of high-energy-de...Understanding the complex plasma dynamics in ultra-intense relativistic laser-solid interactions is of fundamental importance for applications of laser-plasma-based particle accelerators,the creation of high-energy-density matter,understanding planetary science,and laser-driven fusion energy.However,experimental efforts in this regime have been limited by the lack of accessibility of over-critical densities and the poor spatiotemporal resolution of conventional diagnostics.Over the last decade,the advent of femtosecond brilliant hard X-ray free-electron lasers(XFELs)has opened new horizons to overcome these limitations.Here,for the first time,we present full-scale spatiotemporal measurements of solid-density plasma dynamics,including preplasma generation with tens of nanometer scale length driven by the leading edge of a relativistic laser pulse,ultrafast heating and ionization at the main pulse arrival,the laser-driven blast wave,and transient surface return current-induced compression dynamics up to hundreds of picoseconds after interaction.These observations are enabled by utilizing a novel combination of advanced X-ray diagnostics including small-angle X-ray scattering,resonant X-ray emission spectroscopy,and propagation-based X-ray phase-contrast imaging simultaneously at the European XFEL-HED beamline station.展开更多
The molecular composition and biomarker distribution of various occurrences of organic matter in argillaceous source rocks developed in fresh and saline lacustrine environments were revealed by successive treatments o...The molecular composition and biomarker distribution of various occurrences of organic matter in argillaceous source rocks developed in fresh and saline lacustrine environments were revealed by successive treatments of solvent extraction followed by acid hydrolysis using gas chromatography–mass spectrometry. The free fraction obtained by solvent extraction provided abundant geochemical information concerning the sedimentary environment, thermal maturity and biogenic origin, and obvious differences existed between fresh and saline lacustrine source rock samples. Our research results indicate that the carbonate-mineral-bound(CM-bound) fraction released by successive acid hydrolysis could also serve as a significant biogenic indicator, as the bicyclic sesquiterpenoids, indicative of Botryococcus braunii origin, were specifically detected in quite high abundance in the acid-soluble fraction. In addition, the light end hydrocarbons were much better preserved in the acid-soluble fraction, and elemental sulfur was only detected in the CM-bound fraction, suggesting a relatively confined environment for the CM-bound fraction, which thus could preserve additional geochemical information compared to that of the free fraction. The CM-bound fraction also exhibited discernable differences between fresh and saline lacustrine samples. Therefore, it can be concluded that comprehensive analysis of free and CM-bound fractions in the argillaceous source rocks can provide a more authentic and objective interpretation of geologic conditions.展开更多
A free boundary problem for the one-dimensional compressible Navier-Stokes equations is investigated. The asymptotic behavior of solutions toward the superposition of contact discontinuity and shock wave is establishe...A free boundary problem for the one-dimensional compressible Navier-Stokes equations is investigated. The asymptotic behavior of solutions toward the superposition of contact discontinuity and shock wave is established under some smallness conditions. To do this, we first construct a new viscous contact wave such that the momentum equation is satisfied exactly and then determine the shift of the viscous shock wave. By using them together with an inequality concerning the heat kernel in the half space, we obtain the desired a priori estimates. The proof is based on the elementary energy method by the anti-derivative argument.展开更多
This paper is concerned with the free boundary value problem for multidimensional Navier-Stokes equations with density-dependent viscosity where the flow density vanishes continuously across the free boundary. Local ...This paper is concerned with the free boundary value problem for multidimensional Navier-Stokes equations with density-dependent viscosity where the flow density vanishes continuously across the free boundary. Local （in time） existence of a weak solution is established; in particular, the density is positive and the solution is regular away from the free boundary.展开更多
In this article, we investigate the global stability of the wave patterns with the superposition of viscous contact wave and rarefaction wave for the one-dimensional compressible Navier-Stokes equations with a free bo...In this article, we investigate the global stability of the wave patterns with the superposition of viscous contact wave and rarefaction wave for the one-dimensional compressible Navier-Stokes equations with a free boundary. It is shown that for the ideal polytropic gas, the superposition of the viscous contact wave with rarefaction wave is nonlinearly stable for the free boundary problem under the large initial perturbations for any γ 〉 1 with V being the adiabatic exponent provided that the wave strength is suitably small.展开更多
Vibration of a circular membrane in contact with a fluid has extensive applications in industry. The natural vibration frequencies for the asymmetric free vibra- tion of a circular membrane in contact with a bounded i...Vibration of a circular membrane in contact with a fluid has extensive applications in industry. The natural vibration frequencies for the asymmetric free vibra- tion of a circular membrane in contact with a bounded incompressible fluid are derived in this paper. Considering small oscillations induced by the membrane vibration in an incompressible and inviscid fluid, the velocity potential function is used to describe the fluid field. Two approaches are used to derive the free vibration frequencies of the sys- tem, which include a variational formulation and an approximate solution employing the Rayleigh quotient method. A good correlation is found between free vibration frequencies evaluated by these methods. Finally, the effects of the fluid depth, the mass density, and the radial tension on the free vibration frequencies of the coupled system are investigated.展开更多
A strike reset option is an option that allows its holder to reset the strike price to the prevailing underlying asset price at a moment chosen by the holder. The pricing model of the option can be formulated as a par...A strike reset option is an option that allows its holder to reset the strike price to the prevailing underlying asset price at a moment chosen by the holder. The pricing model of the option can be formulated as a parabolic variational inequality and the optimal reset strategy is the free boundary. The smoothness of the free boundary in some cases was showed in our article published in JDE. We would prove its smoothness in the other case in this paper by a generalized comparison principle for the variational inequality.展开更多
This paper is concerned with the spatial propagation of an SIR epidemic model with nonlocal diffusion and free boundaries describing the evolution of a disease.This model can be viewed as a nonlocal version of the fre...This paper is concerned with the spatial propagation of an SIR epidemic model with nonlocal diffusion and free boundaries describing the evolution of a disease.This model can be viewed as a nonlocal version of the free boundary problem studied by Kim et al.(An SIR epidemic model with free boundary.Nonlinear Anal RWA,2013,14:1992-2001).We first prove that this problem has a unique solution defined for all time,and then we give sufficient conditions for the disease vanishing and spreading.Our result shows that the disease will not spread if the basic reproduction number R_(0)<1,or the initial infected area h_(0),expanding ability μ and the initial datum S_(0) are all small enough when 1<R_(0)<1+d/μ_(2)+α.Furthermore,we show that if 1<R_(0)<1+d/μ_(2)+α,the disease will spread when h_(0) is large enough or h_(0) is small but μ is large enough.It is expected that the disease will always spread when R_(0)≥1+d/μ_(2)+α which is different from the local model.展开更多
In this paper, we study a free boundary value problem for two-phase liquid- gas model with mass-dependent viscosity coefficient when both the initial liquid and gas masses connect to vacuum continuously. The gas is as...In this paper, we study a free boundary value problem for two-phase liquid- gas model with mass-dependent viscosity coefficient when both the initial liquid and gas masses connect to vacuum continuously. The gas is assumed to be polytropic whereas the liquid is treated as an incompressible fluid. We give the proof of the global existence and uniqueness of weak solutions whenβ∈ （0, 1）, which have improved the result of Evje and Karlsen, and we obtain the regularity of the solutions by energy method.展开更多
In this article, we consider the free boundary value problem of 3D isentropic compressible Navier-Stokes equations. A blow-up criterion in terms of the maximum norm of gradients of velocity is obtained for the spheric...In this article, we consider the free boundary value problem of 3D isentropic compressible Navier-Stokes equations. A blow-up criterion in terms of the maximum norm of gradients of velocity is obtained for the spherically symmetric strong solution in terms of the regularity estimates near the symmetric center and the free boundary respectively.展开更多
A mathematic model of Green function is build for two dimension free water surface. The analytic expression of Green function is obtained by introducing a parameter of complex number. The intrinsic properties of Green...A mathematic model of Green function is build for two dimension free water surface. The analytic expression of Green function is obtained by introducing a parameter of complex number. The intrinsic properties of Green function are discussed for the special parameter values. The real and imaginary parts of H function are shown in the paper.展开更多
In this paper we consider the nonstationary 1D flow of the compressible viscous and heat-conducting micropolar fluid, assuming that it is in the thermodynamically sense perfect and polytropic. The fluid is between a s...In this paper we consider the nonstationary 1D flow of the compressible viscous and heat-conducting micropolar fluid, assuming that it is in the thermodynamically sense perfect and polytropic. The fluid is between a static solid wall and a free boundary connected to a vacuum state. We take the homogeneous boundary conditions for velocity, microrotation and heat flux on the solid border and that the normal stress, heat flux and microrotation are equal to zero on the free boundary. The proof of the global existence of the solution is based on a limit procedure. We define the finite difference approximate equations system and construct the sequence of approximate solutions that converges to the solution of our problem globally in time.展开更多
In this paper, we investigate the free boundary value problem （FBVP） for the cylindrically symmetric isentropic compressible Navier-Stokes equations （CNS） with density- dependent viscosity coefficients in the case...In this paper, we investigate the free boundary value problem （FBVP） for the cylindrically symmetric isentropic compressible Navier-Stokes equations （CNS） with density- dependent viscosity coefficients in the case that across the free surface stress tensor is balanced by a constant exterior pressure. Under certain assumptions imposed on the initial data, we prove that there exists a unique global strong solution which tends pointwise to a non-vacuum equilibrium state at an exponential time-rate as the time tends to infinity.展开更多
This paper is concerned with the Navier-Stokes/Allen-Cahn system,which is used to model the dynamics of immiscible two-phase flows.We consider a 1D free boundary problem and assume that the viscosity coefficient depen...This paper is concerned with the Navier-Stokes/Allen-Cahn system,which is used to model the dynamics of immiscible two-phase flows.We consider a 1D free boundary problem and assume that the viscosity coefficient depends on the density in the form ofη(ρ)=ρ^(α).The existence of unique global H^(2m)-solutions(m∈N)to the free boundary problem is proven for when 0<α<1/4.Furthermore,we obtain the global C^(∞)-solutions if the initial data is smooth.展开更多
基金Supported by National Natural Science Foundation of China(12101482)Postdoctoral Science Foundation of China(2022M722604)+2 种基金General Project of Science and Technology of Shaanxi Province(2023-YBSF-372)The Natural Science Foundation of Shaan Xi Province(2023-JCQN-0016)Shannxi Mathmatical Basic Science Research Project(23JSQ042)。
文摘In order to better describe the phenomenon of biological invasion,this paper introduces a free boundary model of biological invasion.Firstly,the right free boundary is added to the equation with logistic terms.Secondly,the existence and uniqueness of local solutions are proved by the Sobolev embedding theorem and the comparison principle.Finally,according to the relevant research data and contents of red fire ants,the diffusion area and nest number of red fire ants were simulated without external disturbance.This paper mainly simulates the early diffusion process of red fire ants.In the early diffusion stage,red fire ants grow slowly and then spread over a large area after reaching a certain number.
基金Supported by Zhejiang Provincial Natural Science Foundation of China(No.ZCLQN25A0103)。
文摘This paper studies certain estimates for the lower bound of distance between unitary orbits of normal elements.We show that the distance between unitary orbits of normal elements of simple C^(*)-algebras of tracial rank no more than k has a lower bound.Furthermore,if k≤1 and normal elements are commuting,then the lower bound will be better.Another result establishes a connection involving the spectrum distance operator Dc between a C^(*)-algebra of stable rank one C^(*)-algebra and its hereditary C^(*)-subalgebra.
基金supported by the National Natural Science Foundation of China(Grant No.52071094).
文摘The weakly compressible smooth particle hydrodynamics(WCSPH)model is studied to address the boundary pressure instability of the SPH method,resulting in the development of the SPH method with improved dynamic boundary conditions.This method employs the‘fan’search method for free surface detection,effectively identifying cavity interface particles with diameters smaller than the support domain’s radius,thereby indirectly enhancing the algorithm’s accuracy.On this basis,an improved dynamic boundary condition is proposed by updating the boundary particle pressure calculation scheme to achieve a more stable and continuous pressure field,thereby effectively preventing particles from penetrating the boundary.The SPH method with improved dynamic boundary conditions is used to simulate typical high-speed impact problems such as wedge entry and dam break.The simulation results are in good agreement with the experimental data and other numerical results.
基金Supported by the National Natural Science Foundation of China(Grant Nos.12361040,12061064)the National Science Foundation of Gansu Province(Grant No.22JR5RA264)State Scholarship Fund(Grant No.20230862021).
文摘In this article,we show the existence,uniqueness and stability of bounded solutions to the following quasilinear problems with mean curvature operator(φ'(x′(t)))′=f(t,x),t≥t_(0),lim_(t→∞)x(t)=ψ_(0),lim_(t→∞)x′(t)e^(t)=0,where t_(0) and ψ_(0) are real constants,φ(s)=s/√1−s^(2),s∈R with s∈(−1,1),f:[t_(0),∞)×R→R satisfies the Lipschitz or Osgood-type conditions.
基金Supported by the National Key Research Program(No.2024-1129-954-112)National Natural Science Foundation of China(No.52372033)Guangxi Science and Technology Major Program(No.AA24263054)。
文摘Alkali-free SiO_(2)-Al_(2)O_(3)-CaO-MgO with different SiO_(2)/Al_(2)O_(3)mass ratios was prepared by conventional melt quenching method.The glass network structure,thermodynamic properties and elastic modulus changes with SiO_(2)and Al_(2)O_(3)ratios were investigated using various techniques.It is found that when SiO_(2)is replaced by Al_(2)O_(3),the Q^(4) to Q^(3) transition of silicon-oxygen network decreases while the aluminum-oxygen network increases,which result in the transformation of Si-O-Si bonds to Si-O-Al bonds and an increase in glass network connectivity even though the intermolecular bond strength decreases.The glass transition temperature(T_(g))increases continuously,while the thermal expansion coefficient increases and high-temperature viscosity first decreases and then increases.Meanwhile,the elastic modulus values increase from 93 to 102 GPa.This indicates that the elastic modulus is mainly affected by packing factor and dissociation energy,and elements with higher packing factors and dissociation energies supplant those with lower values,resulting in increased rigidity within the glass.
文摘This study examines the effects of friction stir welding(FSW)and post-weld heat treatment(PWHT)on the grain boundary character distribution and corrosion resistance of cross sectional(top and bottom)regions of nickel-and molybdenum-free high-nitrogen austenitic stainless steel(HNASS).FSW at 400 rpm and 30 mm/min resulted in finer grains(4.18μm)and higher coincident site lattice(CSL)boundaries(32.3%)at the top of the stir zone(SZ)due to dynamic recrystallization(DRX).PWHT at 900℃for 1 h led to grain coarsening(12.91μm the bottom SZ)but enhanced CSL boundaries from 24.6%to 30.2%,improving grain boundary stability.PWHT reduced the kernel average misorientation(KAM)by 14.9%in the SZ-top layer and 20.4%in the SZ-bottom layer,accompanied by a 25%decrease in hardness in the SZ-top layer and 26.7%in the SZ-bottom layer,indicating strain recovery and reduced dislocation density.Potentiodynamic polarization tests(PDP)showed a 18%increase in pitting potential and a 76%reduction in corrosion rate after PWHT.The improvement in corrosion resistance is attributed to the increase inΣ3 twin boundaries,which enhance grain boundary stability and reduce susceptibility to localized corrosion.These findings highlight the role of PWHT in refining the microstructure and strengthening corrosion resistance,making HNASS a promising material for demanding applications.
基金partially supported by the Helmholtz Imaging platform through the project“SmartPhase.”。
文摘Understanding the complex plasma dynamics in ultra-intense relativistic laser-solid interactions is of fundamental importance for applications of laser-plasma-based particle accelerators,the creation of high-energy-density matter,understanding planetary science,and laser-driven fusion energy.However,experimental efforts in this regime have been limited by the lack of accessibility of over-critical densities and the poor spatiotemporal resolution of conventional diagnostics.Over the last decade,the advent of femtosecond brilliant hard X-ray free-electron lasers(XFELs)has opened new horizons to overcome these limitations.Here,for the first time,we present full-scale spatiotemporal measurements of solid-density plasma dynamics,including preplasma generation with tens of nanometer scale length driven by the leading edge of a relativistic laser pulse,ultrafast heating and ionization at the main pulse arrival,the laser-driven blast wave,and transient surface return current-induced compression dynamics up to hundreds of picoseconds after interaction.These observations are enabled by utilizing a novel combination of advanced X-ray diagnostics including small-angle X-ray scattering,resonant X-ray emission spectroscopy,and propagation-based X-ray phase-contrast imaging simultaneously at the European XFEL-HED beamline station.
基金funded by NSFC (National Science Foundation of China) No. 41372130
文摘The molecular composition and biomarker distribution of various occurrences of organic matter in argillaceous source rocks developed in fresh and saline lacustrine environments were revealed by successive treatments of solvent extraction followed by acid hydrolysis using gas chromatography–mass spectrometry. The free fraction obtained by solvent extraction provided abundant geochemical information concerning the sedimentary environment, thermal maturity and biogenic origin, and obvious differences existed between fresh and saline lacustrine source rock samples. Our research results indicate that the carbonate-mineral-bound(CM-bound) fraction released by successive acid hydrolysis could also serve as a significant biogenic indicator, as the bicyclic sesquiterpenoids, indicative of Botryococcus braunii origin, were specifically detected in quite high abundance in the acid-soluble fraction. In addition, the light end hydrocarbons were much better preserved in the acid-soluble fraction, and elemental sulfur was only detected in the CM-bound fraction, suggesting a relatively confined environment for the CM-bound fraction, which thus could preserve additional geochemical information compared to that of the free fraction. The CM-bound fraction also exhibited discernable differences between fresh and saline lacustrine samples. Therefore, it can be concluded that comprehensive analysis of free and CM-bound fractions in the argillaceous source rocks can provide a more authentic and objective interpretation of geologic conditions.
基金partially supported by NSFC (10825102)for distinguished youth scholarsupported by the CAS-TWAS postdoctoral fellowships (FR number:3240223274)AMSS in Chinese Academy of Sciences
文摘A free boundary problem for the one-dimensional compressible Navier-Stokes equations is investigated. The asymptotic behavior of solutions toward the superposition of contact discontinuity and shock wave is established under some smallness conditions. To do this, we first construct a new viscous contact wave such that the momentum equation is satisfied exactly and then determine the shift of the viscous shock wave. By using them together with an inequality concerning the heat kernel in the half space, we obtain the desired a priori estimates. The proof is based on the elementary energy method by the anti-derivative argument.
基金partially supported by the NSFC(10871134)the AHRDIHL Project of Beijing Municipality (PHR201006107)
文摘This paper is concerned with the free boundary value problem for multidimensional Navier-Stokes equations with density-dependent viscosity where the flow density vanishes continuously across the free boundary. Local （in time） existence of a weak solution is established; in particular, the density is positive and the solution is regular away from the free boundary.
基金supported by NSFC Grant No.11171153supported by NSFC Grant No.11322106supported by the Fundamental Research Funds for the Central Universities No.2015ZCQ-LY-01 and No.BLX2015-27
文摘In this article, we investigate the global stability of the wave patterns with the superposition of viscous contact wave and rarefaction wave for the one-dimensional compressible Navier-Stokes equations with a free boundary. It is shown that for the ideal polytropic gas, the superposition of the viscous contact wave with rarefaction wave is nonlinearly stable for the free boundary problem under the large initial perturbations for any γ 〉 1 with V being the adiabatic exponent provided that the wave strength is suitably small.
文摘Vibration of a circular membrane in contact with a fluid has extensive applications in industry. The natural vibration frequencies for the asymmetric free vibra- tion of a circular membrane in contact with a bounded incompressible fluid are derived in this paper. Considering small oscillations induced by the membrane vibration in an incompressible and inviscid fluid, the velocity potential function is used to describe the fluid field. Two approaches are used to derive the free vibration frequencies of the sys- tem, which include a variational formulation and an approximate solution employing the Rayleigh quotient method. A good correlation is found between free vibration frequencies evaluated by these methods. Finally, the effects of the fluid depth, the mass density, and the radial tension on the free vibration frequencies of the coupled system are investigated.
基金supported by National Natural Science Foundation of China(10901060,10971073,1081056)Natural Science Foundation of Guangdong Province (9451063101002091)
文摘A strike reset option is an option that allows its holder to reset the strike price to the prevailing underlying asset price at a moment chosen by the holder. The pricing model of the option can be formulated as a parabolic variational inequality and the optimal reset strategy is the free boundary. The smoothness of the free boundary in some cases was showed in our article published in JDE. We would prove its smoothness in the other case in this paper by a generalized comparison principle for the variational inequality.
基金Zhao was supported by a scholarship from the China Scholarship Council,Li was partially supported by NSF of China(11731005)Cao was partially supported by NSF of China(11901264).
文摘This paper is concerned with the spatial propagation of an SIR epidemic model with nonlocal diffusion and free boundaries describing the evolution of a disease.This model can be viewed as a nonlocal version of the free boundary problem studied by Kim et al.(An SIR epidemic model with free boundary.Nonlinear Anal RWA,2013,14:1992-2001).We first prove that this problem has a unique solution defined for all time,and then we give sufficient conditions for the disease vanishing and spreading.Our result shows that the disease will not spread if the basic reproduction number R_(0)<1,or the initial infected area h_(0),expanding ability μ and the initial datum S_(0) are all small enough when 1<R_(0)<1+d/μ_(2)+α.Furthermore,we show that if 1<R_(0)<1+d/μ_(2)+α,the disease will spread when h_(0) is large enough or h_(0) is small but μ is large enough.It is expected that the disease will always spread when R_(0)≥1+d/μ_(2)+α which is different from the local model.
基金Supported by the National Natural Science Foundation of China (11171340)
文摘In this paper, we study a free boundary value problem for two-phase liquid- gas model with mass-dependent viscosity coefficient when both the initial liquid and gas masses connect to vacuum continuously. The gas is assumed to be polytropic whereas the liquid is treated as an incompressible fluid. We give the proof of the global existence and uniqueness of weak solutions whenβ∈ （0, 1）, which have improved the result of Evje and Karlsen, and we obtain the regularity of the solutions by energy method.
基金supported by the NNSFC(11171228,11231006,and 11225102)NSFC-RGC Grant 11461161007the Key Project of Beijing Municipal Education Commission No.CIT&TCD20140323
文摘In this article, we consider the free boundary value problem of 3D isentropic compressible Navier-Stokes equations. A blow-up criterion in terms of the maximum norm of gradients of velocity is obtained for the spherically symmetric strong solution in terms of the regularity estimates near the symmetric center and the free boundary respectively.
文摘A mathematic model of Green function is build for two dimension free water surface. The analytic expression of Green function is obtained by introducing a parameter of complex number. The intrinsic properties of Green function are discussed for the special parameter values. The real and imaginary parts of H function are shown in the paper.
基金supported by Scientific Research of the University of Rijeka(13.14.1.3.03)
文摘In this paper we consider the nonstationary 1D flow of the compressible viscous and heat-conducting micropolar fluid, assuming that it is in the thermodynamically sense perfect and polytropic. The fluid is between a static solid wall and a free boundary connected to a vacuum state. We take the homogeneous boundary conditions for velocity, microrotation and heat flux on the solid border and that the normal stress, heat flux and microrotation are equal to zero on the free boundary. The proof of the global existence of the solution is based on a limit procedure. We define the finite difference approximate equations system and construct the sequence of approximate solutions that converges to the solution of our problem globally in time.
基金supported by NNSFC(11101145),supported by NNSFC(11326140 and11501323)China Postdoctoral Science Foundation(2012M520360)+1 种基金Doctoral Foundation of North China University of Water Sources and Electric Power(201032),Innovation Scientists and Technicians Troop Construction Projects of Henan Provincethe Doctoral Starting up Foundation of Quzhou University(BSYJ201314 and XNZQN201313)
文摘In this paper, we investigate the free boundary value problem （FBVP） for the cylindrically symmetric isentropic compressible Navier-Stokes equations （CNS） with density- dependent viscosity coefficients in the case that across the free surface stress tensor is balanced by a constant exterior pressure. Under certain assumptions imposed on the initial data, we prove that there exists a unique global strong solution which tends pointwise to a non-vacuum equilibrium state at an exponential time-rate as the time tends to infinity.
基金supported by the Key Project of the NSFC(12131010)the NSFC(11771155,12271032)+1 种基金the NSF of Guangdong Province(2021A1515010249,2021A1515010303)supported by the NSFC(11971179,12371205)。
文摘This paper is concerned with the Navier-Stokes/Allen-Cahn system,which is used to model the dynamics of immiscible two-phase flows.We consider a 1D free boundary problem and assume that the viscosity coefficient depends on the density in the form ofη(ρ)=ρ^(α).The existence of unique global H^(2m)-solutions(m∈N)to the free boundary problem is proven for when 0<α<1/4.Furthermore,we obtain the global C^(∞)-solutions if the initial data is smooth.
