In this paper,we consider the following spatial Solow-Swan model with density-dependent motion■whereσ>0,α∈(0,1)andΩ⊂ℝn(n≥1)is a bounded domain with smooth boundary andϕ∈C3([0,∞)),ϕ(s)>0 for all s≥0.We p...In this paper,we consider the following spatial Solow-Swan model with density-dependent motion■whereσ>0,α∈(0,1)andΩ⊂ℝn(n≥1)is a bounded domain with smooth boundary andϕ∈C3([0,∞)),ϕ(s)>0 for all s≥0.We prove that if■then there exists a unique time-globally classical solution(u,v)for all n≥1,such a solution is bounded and satisfies u≥0,v>0.Moreover,we show that the above solution will convergence to the steady state(1,1)exponentially in L^(∞)as t→∞.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
In this paper, we consider the global existence of classical solution to the 3-D compressible Navier-Stokes equations with a density-dependent viscosity coefficient λ(ρ)provided that the initial energy is small in s...In this paper, we consider the global existence of classical solution to the 3-D compressible Navier-Stokes equations with a density-dependent viscosity coefficient λ(ρ)provided that the initial energy is small in some sense. In our result, we give a relation between the initial energy and the viscosity coefficient μ, and it shows that the initial energy can be large if the coefficient of the viscosity μ is taken to be large, which implies that large viscosity μ means large solution.展开更多
We study the large-time behavior toward viscous shock waves to the Cauchy problem of the one-dimensional compressible isentropic Navier-Stokes equations with density- dependent viscosity. The nonlinear stability of th...We study the large-time behavior toward viscous shock waves to the Cauchy problem of the one-dimensional compressible isentropic Navier-Stokes equations with density- dependent viscosity. The nonlinear stability of the viscous shock waves is shown for certain class of large initial perturbation with integral zero which can allow the initial density to have large oscillation. Our analysis relies upon the technique developed by Kanel~ and the continuation argument.展开更多
In this article, a special type of fractional differential equations(FDEs) named the density-dependent conformable fractional diffusion-reaction(DDCFDR) equation is studied. Aforementioned equation has a significant r...In this article, a special type of fractional differential equations(FDEs) named the density-dependent conformable fractional diffusion-reaction(DDCFDR) equation is studied. Aforementioned equation has a significant role in the modelling of some phenomena arising in the applied science. The well-organized methods, including the exp(-φ(ε))-expansion and modified Kudryashov methods are exerted to generate the exact solutions of this equation such that some of the solutions are new and have been reported for the first time. Results illustrate that both methods have a great performance in handling the DDCFDR equation.展开更多
In this paper,we consider the 3D compressible isentropic Navier-Stokes equations when the shear viscosityμis a positive constant and the bulk viscosity is λ(ρ)=ρ^(β) with β>2,which is a situation that was fir...In this paper,we consider the 3D compressible isentropic Navier-Stokes equations when the shear viscosityμis a positive constant and the bulk viscosity is λ(ρ)=ρ^(β) with β>2,which is a situation that was first introduced by Vaigant and Kazhikhov in[1].The global axisymmetric classical solution with arbitrarily large initial data in a periodic domain Ω={(r,z)|r=√x^(2)+y^(2),(x,y,z)∈R^(3),r∈I⊂(0,+∞),-∞<z<+∞} is obtained.Here the initial density keeps a non-vacuum state ρ>0 when z→±∞.Our results also show that the solution will not develop the vacuum state in any finite time,provided that the initial density is uniformly away from the vacuum.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
The global existence of solutions to the equations of one-dimensional compressible flow with density-dependent viscosity is proved. Specifically,the assumptions on initial data are that the modulo constant is stated a...The global existence of solutions to the equations of one-dimensional compressible flow with density-dependent viscosity is proved. Specifically,the assumptions on initial data are that the modulo constant is stated at x=∞ ＋and x=-∞ ,which may be different ,the density and velocity are in L^z ,and the density is bounded above and below away from zero. The results also show that even under these conditions, neither vacuum states nor concentration states can be formed in finite time.展开更多
In this paper,we prove the existence of general Cartesian vector solutions u=b(t)+A(t)x for the Ndimensional compressible Navier–Stokes equations with density-dependent viscosity,based on the matrix and curve integra...In this paper,we prove the existence of general Cartesian vector solutions u=b(t)+A(t)x for the Ndimensional compressible Navier–Stokes equations with density-dependent viscosity,based on the matrix and curve integration theory.Two exact solutions are obtained by solving the reduced systems.展开更多
This paper is devoted to studying the zero dissipation limit problem for the one-dimensional compressible Navier-Stokes equations with selected density-dependent viscosity.In particular,we focus our attention on the v...This paper is devoted to studying the zero dissipation limit problem for the one-dimensional compressible Navier-Stokes equations with selected density-dependent viscosity.In particular,we focus our attention on the viscosity taking the formμ(ρ)=ρ^(ϵ)(ϵ>0).For the selected density-dependent viscosity,it is proved that the solutions of the one-dimensional compressible Navier-Stokes equations with centered rarefaction wave initial data exist for all time,and converge to the centered rarefaction waves as the viscosity vanishes,uniformly away from the initial discontinuities.New and subtle analysis is developed to overcome difficulties due to the selected density-dependent viscosity to derive energy estimates,in addition to the scaling argument and elementary energy analysis.Moreover,our results extend the studies in[Xin Z P.Comm Pure Appl Math,1993,46(5):621-665].展开更多
This paper is concerned with the asymptotic behavior of solutions to the initial boundary problem of the two-dimensional density-dependent Boussinesq equations.It is shown that the solutions of the Boussinesq equation...This paper is concerned with the asymptotic behavior of solutions to the initial boundary problem of the two-dimensional density-dependent Boussinesq equations.It is shown that the solutions of the Boussinesq equations converge to those of zero thermal diffusivity Boussinesq equations as the thermal diffusivity tends to zero,and the convergence rate is established.In addition,we prove that the boundary-layer thickness is of the valueδ(k)=k^(α)with anyα∈(0,1/4)for a small diffusivity coefficient k>0,and we also find a function to describe the properties of the boundary layer.展开更多
In the mean field approximation of nonlinear relativistic a-ω-p model, we have studied the influence of density-dependent coupling constants between nucleons and mesons on the equation of state （EOS） of infinite sy...In the mean field approximation of nonlinear relativistic a-ω-p model, we have studied the influence of density-dependent coupling constants between nucleons and mesons on the equation of state （EOS） of infinite symmetric nuclear matter in different conditions. We find that the EOS of nuclear matter will become stiffer as e, d in the self- interaction of σ meson increase when the coeffcients except aω in Гω, in which the opposite occurs, are fixed. On the other hand, greater values of aσ, bσ, cσ, aω, dω and smaller values of dσ, bω, cω will lead to stiffer EOS ifc and d are fixed. Besides, greater values of Гω lead to stiffer EOS in high density region for the EOS with same incompressibility coefficient at saturation density.展开更多
We consider the Cauchy problem, free boundary problem and piston problem for one-dimensional compressible Navier-Stokes equations with density-dependent viscosity. Using the reduction to absurdity method, we prove tha...We consider the Cauchy problem, free boundary problem and piston problem for one-dimensional compressible Navier-Stokes equations with density-dependent viscosity. Using the reduction to absurdity method, we prove that the weak solutions to these systems do not exhibit vacuum states, provided that no vacuum states are present initially. The essential re- quirements on the solutions are that the mass and energy of the fluid are locally integrable at each time, and the Lloc1-norm of the velocity gradient is locally integrable in time.展开更多
Population changes are believed to be controlled by multiple factors, including an important density-dependent effect. This paper reviews the literature on this topic and shows that this density-dependent effect does ...Population changes are believed to be controlled by multiple factors, including an important density-dependent effect. This paper reviews the literature on this topic and shows that this density-dependent effect does not exist. This paper also gives a typical example in which no density-dependent effect was detected in the stock-recruitment relationship in Japanese sardines. The recruitment was found to be determined in proportion to the spawning stock biomass and to be affected by environmental factors. This simple mechanism is applicable not only in fish species but also in insects such as Thrips imaginis in Australia. The reason that many biologists have not become aware that the density-dependent effect does not exist is discussed using a metaphor. This paper proposes a new concept in the study of population change. The new concept proposed here will replace the currently used basic concept that has been assumed to be correct for more than 50 years.展开更多
In this paper we are interested in the large time behavior of the nonlinear diffusion equationWe consider functions which allow the equation to possess traveling wave solutions. We first present an existence and uniqu...In this paper we are interested in the large time behavior of the nonlinear diffusion equationWe consider functions which allow the equation to possess traveling wave solutions. We first present an existence and uniqueness as well as some comparison principle result of generalized solutions to the Cauchy problem. Then we give for some threshold results, from which we can see that u=a is stable, while u= 0 or u=1 is unstable under some assumptions, etc.展开更多
This paper studies the existence and uniqueness of local strong solutions to an Oldroyd-B model with density-dependent viscosity in a bounded domain Ω ⊂ R<sup>d</sup>, d = 2 or 3 via incompressible limit,...This paper studies the existence and uniqueness of local strong solutions to an Oldroyd-B model with density-dependent viscosity in a bounded domain Ω ⊂ R<sup>d</sup>, d = 2 or 3 via incompressible limit, in which the initial data is “well-prepared” and the velocity field enjoys the slip boundary conditions. The main idea is to derive the uniform energy estimates for nonlinear systems and corresponding incompressible limit.展开更多
The symmetry energy which characterizes the isospin dependence of the equation of state of asymmetric nuclearmatter, plays a crucial role in understanding a variety of issues in nuclear physics and astrophysics, such ...The symmetry energy which characterizes the isospin dependence of the equation of state of asymmetric nuclearmatter, plays a crucial role in understanding a variety of issues in nuclear physics and astrophysics, such as heavyion collisions, exotic nuclei, stability of superheavy nuclei, fusion cross sections, the structures, composition andcooling of neutron stars[1??5]. Much theoretical and experimental effort has been made to constrain the densitydependence of symmetry energy. Up to now, we have got some basic knowledge about the symmetry energy at lowdensities, while at high densities we even do not know its variation tendency as a function of density. The problemremains unsolved due to the difficulty of nucleon-nucleon interactions and many-body problems.展开更多
This paper studies an Ebola epidemic model with an exponential nonlinear incidence function that considers the efficacy and the behaviour change.The current model also incorporates a new density-dependent treatment th...This paper studies an Ebola epidemic model with an exponential nonlinear incidence function that considers the efficacy and the behaviour change.The current model also incorporates a new density-dependent treatment that catches the impact of the disease transmission on the treatment.Firstly,we provide a theoretical study of the nonlinear differential equations model obtained.More precisely,we derive the effective reproduction number and,under suitable conditions,prove the stability of equilibria.Afterwards,we show that the model exhibits the phenomenon of backward-bifurcation whenever the bifurcation parameter and the reproduction number are less than one.We find that the bi-stability and backward-bifurcation are not automatically connected in epidemic models.In fact,when a backward-bifurcation occurs,the disease-free equilibrium may be globally stable.Numerically,we use well-known standard tools to fit the model to the data reported for the 2018–2020 Kivu Ebola outbreak,and perform the sensitivity analysis.To control Ebola epidemics,our findings recommend a combination of a rapid behaviour change and the implementation of a proper treatment strategy with a high level of efficacy.Secondly,we propose and analyze a fractional-order Ebola epidemic model,which is an extension of the first model studied.We use the Caputo operator and construct the Grünwald-Letnikov nonstandard finite difference scheme,and show its advantages.展开更多
The neutron star as a supernova remnant is attracting high attention recently due to the gravitation wave detection and precise measurements about its mass and radius.In particular,the compact object with a mass of 2....The neutron star as a supernova remnant is attracting high attention recently due to the gravitation wave detection and precise measurements about its mass and radius.In particular,the compact object with a mass of 2.50-2.67 M_(⊙)observed by LIGO Scientific and Virgo collaborations in GW190814,as well as the recent report of a light compact object with a mass and radius of M=0.77_(-0.17)^(+0.20)M_(⊙)and R=10.4_(-0.78)^(+0.86)km within the supernova remnant HESS J1731-347,have posed a great challenge to the investigations into the supranuclear matter.In the inner core of a neutron star,the strangeness degrees of freedom,such as the hyperons,can be present to form a hyperon star.In this work,the neutron star consisting of nucleons and leptons,and the hyperonic star including the hyperons will be studied in the framework of the density-dependent relativistic mean-field(DDRMF)model.Some popular DDRMF parameterizations will be adopted to investigate the properties of nuclear matter and the mass,radius,tidal deformability,and other properties of neutron star and hyperonic stars.We find that the maximum masses of neutron star calculated by DD-MEX,DD-MEX1,DD-MEX2,DD-MEXY and DD-LZ1 sets can be around 2.5-2.6 MM_(⊙)because they can produce quite stiff equations of state(EOSs)due to the strong repulsive contributions from vector potentials at high densities.Moreover,by investigating the influence of the crust EOS and core EOS on the neutron stars,we find that the observational data from HESS J1731-347 suggest the requirement of a crust EOS with a higher L parameter and a core EOS with a lower L parameter,and the M-R relations from the constructed EOSs can also be consistent with the observables of PSR J0740+6620,PSR J0030+0451 from NICER and the GW170817 event.With the inclusion of hyperons,the hyperonic star matter becomes softer compared to the neutron star matter,but the massive hyperonic star can also be obtained with DDRMF parameter sets if the vector meson coupling constants are strong.展开更多
The Navier-Stokes system for one-dimensional compressible fluids with density-dependent viscosities when the initial density connects to vacuum continuously is considered in the present paper. When the viscosity coeff...The Navier-Stokes system for one-dimensional compressible fluids with density-dependent viscosities when the initial density connects to vacuum continuously is considered in the present paper. When the viscosity coefficient u is proportional to pθ with 0 〈 θ 〈 1, the global existence and the uniqueness of weak solutions are proved which improves the previous results in [Vong, S. W., Yang, T., Zhu, C. J.： Compressible Navier-Stokes equations with degenerate viscosity coefficient and vacuum II. J. Differential Equations, 192（2）, 475-501 （2003）]. Here p is the density. Moreover, a stabilization rate estimate for the density as t → ＋∞ for any θ 〉 0 is also given.展开更多
基金supported by the Jilin Scientific and Technological Development Program(20210101466JC).
文摘In this paper,we consider the following spatial Solow-Swan model with density-dependent motion■whereσ>0,α∈(0,1)andΩ⊂ℝn(n≥1)is a bounded domain with smooth boundary andϕ∈C3([0,∞)),ϕ(s)>0 for all s≥0.We prove that if■then there exists a unique time-globally classical solution(u,v)for all n≥1,such a solution is bounded and satisfies u≥0,v>0.Moreover,we show that the above solution will convergence to the steady state(1,1)exponentially in L^(∞)as t→∞.
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.
文摘In this paper, we consider the global existence of classical solution to the 3-D compressible Navier-Stokes equations with a density-dependent viscosity coefficient λ(ρ)provided that the initial energy is small in some sense. In our result, we give a relation between the initial energy and the viscosity coefficient μ, and it shows that the initial energy can be large if the coefficient of the viscosity μ is taken to be large, which implies that large viscosity μ means large solution.
基金supported by"the Fundamental Research Funds for the Central Universities"
文摘We study the large-time behavior toward viscous shock waves to the Cauchy problem of the one-dimensional compressible isentropic Navier-Stokes equations with density- dependent viscosity. The nonlinear stability of the viscous shock waves is shown for certain class of large initial perturbation with integral zero which can allow the initial density to have large oscillation. Our analysis relies upon the technique developed by Kanel~ and the continuation argument.
文摘In this article, a special type of fractional differential equations(FDEs) named the density-dependent conformable fractional diffusion-reaction(DDCFDR) equation is studied. Aforementioned equation has a significant role in the modelling of some phenomena arising in the applied science. The well-organized methods, including the exp(-φ(ε))-expansion and modified Kudryashov methods are exerted to generate the exact solutions of this equation such that some of the solutions are new and have been reported for the first time. Results illustrate that both methods have a great performance in handling the DDCFDR equation.
基金supported by NNSFC(11701443,11901444,11931013)Natural Science Basic Research Plan in Shaanxi Province of China(2019JQ-870)。
文摘In this paper,we consider the 3D compressible isentropic Navier-Stokes equations when the shear viscosityμis a positive constant and the bulk viscosity is λ(ρ)=ρ^(β) with β>2,which is a situation that was first introduced by Vaigant and Kazhikhov in[1].The global axisymmetric classical solution with arbitrarily large initial data in a periodic domain Ω={(r,z)|r=√x^(2)+y^(2),(x,y,z)∈R^(3),r∈I⊂(0,+∞),-∞<z<+∞} is obtained.Here the initial density keeps a non-vacuum state ρ>0 when z→±∞.Our results also show that the solution will not develop the vacuum state in any finite time,provided that the initial density is uniformly away from the vacuum.
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.
文摘The global existence of solutions to the equations of one-dimensional compressible flow with density-dependent viscosity is proved. Specifically,the assumptions on initial data are that the modulo constant is stated at x=∞ ＋and x=-∞ ,which may be different ,the density and velocity are in L^z ,and the density is bounded above and below away from zero. The results also show that even under these conditions, neither vacuum states nor concentration states can be formed in finite time.
基金This research is partially supported by the National Science Foundation of China(Grant No.11271079,10671095)RG 11/2015-2016R from the Education University of Hong Kong。
文摘In this paper,we prove the existence of general Cartesian vector solutions u=b(t)+A(t)x for the Ndimensional compressible Navier–Stokes equations with density-dependent viscosity,based on the matrix and curve integration theory.Two exact solutions are obtained by solving the reduced systems.
基金supported by the National Natural Science Foundation of China(11671319,11931013).
文摘This paper is devoted to studying the zero dissipation limit problem for the one-dimensional compressible Navier-Stokes equations with selected density-dependent viscosity.In particular,we focus our attention on the viscosity taking the formμ(ρ)=ρ^(ϵ)(ϵ>0).For the selected density-dependent viscosity,it is proved that the solutions of the one-dimensional compressible Navier-Stokes equations with centered rarefaction wave initial data exist for all time,and converge to the centered rarefaction waves as the viscosity vanishes,uniformly away from the initial discontinuities.New and subtle analysis is developed to overcome difficulties due to the selected density-dependent viscosity to derive energy estimates,in addition to the scaling argument and elementary energy analysis.Moreover,our results extend the studies in[Xin Z P.Comm Pure Appl Math,1993,46(5):621-665].
基金the National Natural Science Foundation of China(12061037,11971209)the Natural Science Foundation of Jiangxi Province(20212BAB201016)National Natural Science Foundation of China(11861038)。
文摘This paper is concerned with the asymptotic behavior of solutions to the initial boundary problem of the two-dimensional density-dependent Boussinesq equations.It is shown that the solutions of the Boussinesq equations converge to those of zero thermal diffusivity Boussinesq equations as the thermal diffusivity tends to zero,and the convergence rate is established.In addition,we prove that the boundary-layer thickness is of the valueδ(k)=k^(α)with anyα∈(0,1/4)for a small diffusivity coefficient k>0,and we also find a function to describe the properties of the boundary layer.
基金Supported by the National Natural Science Foundation of China under Grant No.11275073
文摘In the mean field approximation of nonlinear relativistic a-ω-p model, we have studied the influence of density-dependent coupling constants between nucleons and mesons on the equation of state （EOS） of infinite symmetric nuclear matter in different conditions. We find that the EOS of nuclear matter will become stiffer as e, d in the self- interaction of σ meson increase when the coeffcients except aω in Гω, in which the opposite occurs, are fixed. On the other hand, greater values of aσ, bσ, cσ, aω, dω and smaller values of dσ, bω, cω will lead to stiffer EOS ifc and d are fixed. Besides, greater values of Гω lead to stiffer EOS in high density region for the EOS with same incompressibility coefficient at saturation density.
基金Project supported by the National Natural Science Foundation of China (No. 10571158) and the DFG
文摘We consider the Cauchy problem, free boundary problem and piston problem for one-dimensional compressible Navier-Stokes equations with density-dependent viscosity. Using the reduction to absurdity method, we prove that the weak solutions to these systems do not exhibit vacuum states, provided that no vacuum states are present initially. The essential re- quirements on the solutions are that the mass and energy of the fluid are locally integrable at each time, and the Lloc1-norm of the velocity gradient is locally integrable in time.
文摘Population changes are believed to be controlled by multiple factors, including an important density-dependent effect. This paper reviews the literature on this topic and shows that this density-dependent effect does not exist. This paper also gives a typical example in which no density-dependent effect was detected in the stock-recruitment relationship in Japanese sardines. The recruitment was found to be determined in proportion to the spawning stock biomass and to be affected by environmental factors. This simple mechanism is applicable not only in fish species but also in insects such as Thrips imaginis in Australia. The reason that many biologists have not become aware that the density-dependent effect does not exist is discussed using a metaphor. This paper proposes a new concept in the study of population change. The new concept proposed here will replace the currently used basic concept that has been assumed to be correct for more than 50 years.
文摘In this paper we are interested in the large time behavior of the nonlinear diffusion equationWe consider functions which allow the equation to possess traveling wave solutions. We first present an existence and uniqueness as well as some comparison principle result of generalized solutions to the Cauchy problem. Then we give for some threshold results, from which we can see that u=a is stable, while u= 0 or u=1 is unstable under some assumptions, etc.
文摘This paper studies the existence and uniqueness of local strong solutions to an Oldroyd-B model with density-dependent viscosity in a bounded domain Ω ⊂ R<sup>d</sup>, d = 2 or 3 via incompressible limit, in which the initial data is “well-prepared” and the velocity field enjoys the slip boundary conditions. The main idea is to derive the uniform energy estimates for nonlinear systems and corresponding incompressible limit.
文摘The symmetry energy which characterizes the isospin dependence of the equation of state of asymmetric nuclearmatter, plays a crucial role in understanding a variety of issues in nuclear physics and astrophysics, such as heavyion collisions, exotic nuclei, stability of superheavy nuclei, fusion cross sections, the structures, composition andcooling of neutron stars[1??5]. Much theoretical and experimental effort has been made to constrain the densitydependence of symmetry energy. Up to now, we have got some basic knowledge about the symmetry energy at lowdensities, while at high densities we even do not know its variation tendency as a function of density. The problemremains unsolved due to the difficulty of nucleon-nucleon interactions and many-body problems.
基金C.Tadmon acknowledges good working conditions at the institute of Mathematics,University of Mainz,where this paper has been finalised during a research stay supported by the Alexander von Humboldt Foundation.
文摘This paper studies an Ebola epidemic model with an exponential nonlinear incidence function that considers the efficacy and the behaviour change.The current model also incorporates a new density-dependent treatment that catches the impact of the disease transmission on the treatment.Firstly,we provide a theoretical study of the nonlinear differential equations model obtained.More precisely,we derive the effective reproduction number and,under suitable conditions,prove the stability of equilibria.Afterwards,we show that the model exhibits the phenomenon of backward-bifurcation whenever the bifurcation parameter and the reproduction number are less than one.We find that the bi-stability and backward-bifurcation are not automatically connected in epidemic models.In fact,when a backward-bifurcation occurs,the disease-free equilibrium may be globally stable.Numerically,we use well-known standard tools to fit the model to the data reported for the 2018–2020 Kivu Ebola outbreak,and perform the sensitivity analysis.To control Ebola epidemics,our findings recommend a combination of a rapid behaviour change and the implementation of a proper treatment strategy with a high level of efficacy.Secondly,we propose and analyze a fractional-order Ebola epidemic model,which is an extension of the first model studied.We use the Caputo operator and construct the Grünwald-Letnikov nonstandard finite difference scheme,and show its advantages.
文摘The neutron star as a supernova remnant is attracting high attention recently due to the gravitation wave detection and precise measurements about its mass and radius.In particular,the compact object with a mass of 2.50-2.67 M_(⊙)observed by LIGO Scientific and Virgo collaborations in GW190814,as well as the recent report of a light compact object with a mass and radius of M=0.77_(-0.17)^(+0.20)M_(⊙)and R=10.4_(-0.78)^(+0.86)km within the supernova remnant HESS J1731-347,have posed a great challenge to the investigations into the supranuclear matter.In the inner core of a neutron star,the strangeness degrees of freedom,such as the hyperons,can be present to form a hyperon star.In this work,the neutron star consisting of nucleons and leptons,and the hyperonic star including the hyperons will be studied in the framework of the density-dependent relativistic mean-field(DDRMF)model.Some popular DDRMF parameterizations will be adopted to investigate the properties of nuclear matter and the mass,radius,tidal deformability,and other properties of neutron star and hyperonic stars.We find that the maximum masses of neutron star calculated by DD-MEX,DD-MEX1,DD-MEX2,DD-MEXY and DD-LZ1 sets can be around 2.5-2.6 MM_(⊙)because they can produce quite stiff equations of state(EOSs)due to the strong repulsive contributions from vector potentials at high densities.Moreover,by investigating the influence of the crust EOS and core EOS on the neutron stars,we find that the observational data from HESS J1731-347 suggest the requirement of a crust EOS with a higher L parameter and a core EOS with a lower L parameter,and the M-R relations from the constructed EOSs can also be consistent with the observables of PSR J0740+6620,PSR J0030+0451 from NICER and the GW170817 event.With the inclusion of hyperons,the hyperonic star matter becomes softer compared to the neutron star matter,but the massive hyperonic star can also be obtained with DDRMF parameter sets if the vector meson coupling constants are strong.
基金supported by National Natural Science Foundation of China (Grant Nos. 10401012, 10771170)supported by (#10625105)the Key Laboratory of Mathematical Physics of Hubei Province
文摘The Navier-Stokes system for one-dimensional compressible fluids with density-dependent viscosities when the initial density connects to vacuum continuously is considered in the present paper. When the viscosity coefficient u is proportional to pθ with 0 〈 θ 〈 1, the global existence and the uniqueness of weak solutions are proved which improves the previous results in [Vong, S. W., Yang, T., Zhu, C. J.： Compressible Navier-Stokes equations with degenerate viscosity coefficient and vacuum II. J. Differential Equations, 192（2）, 475-501 （2003）]. Here p is the density. Moreover, a stabilization rate estimate for the density as t → ＋∞ for any θ 〉 0 is also given.
