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GLOBAL CLASSICAL SOLUTIONS OF 3D COMPRESSIBLE MICROPOLAR FLUIDS WITH FAR-FIELD VACUUM
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作者 Mingyu ZHANG 《Acta Mathematica Scientia》 2025年第3期919-936,共18页
This paper concerns the Cauchy problem of 3D compressible micropolar fluids in the whole space R^(3). For regular initial data with m0E0 is suitable small, where m0 and E0 represent the upper bound of initial density ... This paper concerns the Cauchy problem of 3D compressible micropolar fluids in the whole space R^(3). For regular initial data with m0E0 is suitable small, where m0 and E0 represent the upper bound of initial density and initial energy, we prove that if ρ0 ∈ Lγ ∩ H3 with γ ∈ (1, 6), then the problem possesses a unique global classical solution on R^(3) × [0, T] with any T ∈ (0, ∞). It’s worth noting that both the vacuum states and possible random largeness of initial energy are allowed. 展开更多
关键词 compressible micropolar fluids Cauchy problem global classical solutions s-mall density VACUUM
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Facile synthesis of Na_(0.9)Mg_(0.45)Ti_(3.55)O_(8)-Na_(2)Ni_(2)Ti_(6)O_(16)solid solutions for improving photocatalytic CO_(2)reduction
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作者 WANG Jingzhou YAO Chenzhong +2 位作者 ZHANG Xisheng MA Ziwei LI Linfeng 《燃料化学学报(中英文)》 北大核心 2026年第1期15-25,共11页
In this study,a straightforward one-step hydrothermal method was successfully utilized to synthesize the solid solution Na_(0.9)Mg_(0.45)Ti_(3.55)O_(8)-Na_(2)Ni_(2)Ti_(6)O_(16)(NNMTO-x),where x denotes the molar perce... In this study,a straightforward one-step hydrothermal method was successfully utilized to synthesize the solid solution Na_(0.9)Mg_(0.45)Ti_(3.55)O_(8)-Na_(2)Ni_(2)Ti_(6)O_(16)(NNMTO-x),where x denotes the molar percentage of Na_(2)Ni_(2)Ti_(6)O_(16)(NNTO)within Na_(0.9)Mg_(0.45)Ti_(3.55)O_(8)(NMTO),with x values of 10,20,30,40,and 50.Both XPS(X-ray Photoelectron Spectroscopy)and EDX(Energy Dispersive X-ray Spectroscopy)analyses unequivocally validated the formation of the NNMTO-x solid solutions.It was observed that when x is below 40,the NNMTO-x solid solution retains the structural characteristics of the original NMTO.However,beyond this threshold,significant alterations in crystal morphology were noted,accompanied by a noticeable decline in photocatalytic activity.Notably,the absorption edge of NNMTO-x(x<40)exhibited a shift towards the visible-light spectrum,thereby substantially broadening the absorption range.The findings highlight that NNMTO-30 possesses the most pronounced photocatalytic activity for the reduction of CO_(2).Specifically,after a 6 h irradiation period,the production rates of CO and CH_(4)were recorded at 42.38 and 1.47μmol/g,respectively.This investigation provides pivotal insights that are instrumental in the advancement of highly efficient and stable photocatalysts tailored for CO_(2)reduction processes. 展开更多
关键词 photocatalytic conversion hydrothermal method optical response range solid solution charge separation
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Existence,Uniqueness and Stability of Bounded Solutions for Minkowski-Curvature Problems with Asymptotic Boundary Conditions
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作者 Tianlan CHEN Xuying TANG 《Journal of Mathematical Research with Applications》 2026年第1期57-70,共14页
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
关键词 mean curvature operator UNIQUENESS asymptotic boundary conditions bounded solution
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Solution set of circumlunar abort trajectory and its direct application to optimization design
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作者 Tianshan DONG Zhen HUANG +2 位作者 Wenyan ZHOU Xiangyu ZHANG Lin LU 《Chinese Journal of Aeronautics》 2026年第1期333-348,共16页
Circumlunar abort trajectories constitute a vital contingency return strategy during the translunar phase of crewed lunar missions.This paper proposes a methodology for constructing the solution set of the circumlunar... Circumlunar abort trajectories constitute a vital contingency return strategy during the translunar phase of crewed lunar missions.This paper proposes a methodology for constructing the solution set of the circumlunar abort trajectory and leverages its advantageous properties to address the optimization design problem of abort trajectories.Initially,a solution set of all feasible abort trajectories,originating from an abort point on the nominal trajectory and complying with fundamental reentry constraints,is formulated through the introduction of two novel design parameters.Subsequently,the geometric characteristics of the solution set,as well as the distributional properties of key iterative constraint responses,including flight time and velocity increment,are analyzed.Finally,the characteristics exhibited in the solution set are employed to directly identify the design parameters of the abort trajectories with minimum flight time and velocity increment,thereby providing solutions to two distinct types of optimization problems.The simulation results for a variety of nominal trajectories,encompassing the reconstruction and redesign of the Apollo13 abort trajectory,validate the proposed method,demonstrating its ability to directly generate optimal abort trajectories.The method proposed in this paper investigates feasible abort trajectories from a global perspective,providing both a framework and convenience for mission planning and iterative optimization in abort trajectory design. 展开更多
关键词 Circumlunar abort trajectory Design parameters Geometric characteristics Optimization problems solution set
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Analytical solution for longitudinal responses of tunnels under combined effects of seismic waves and strike-slip faulting
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作者 Jie Tang Manchao He +2 位作者 Yafei Qiao Hanbing Bian Chun Zhu 《Journal of Rock Mechanics and Geotechnical Engineering》 2026年第2期1266-1289,共24页
Strong seismic excitation and fault dislocation are likely to occur simultaneously in high-intensity seismic zones,causing severe damage to tunnels crossing active fault zones.This paper aims to develop a novel analyt... Strong seismic excitation and fault dislocation are likely to occur simultaneously in high-intensity seismic zones,causing severe damage to tunnels crossing active fault zones.This paper aims to develop a novel analytical solution to determine the longitudinal mechanical responses of tunnels subjected to the combined effects of seismic waves and strike-slip faulting.Adopting the elastic springbeam model,the seismic waves are modelled as shear horizontal(SH)waves and the fault dislocation follows an S-shaped pattern;the superposition principle for free-fielddisplacements caused by both effects is assumed.In addition,the transmission and reflectionof seismic waves at the fault-rock geological interface and the tangential contact conditions at the tunnel-rock interface are considered.The analytical model is validated against numerical simulations,confirmingits accuracy in calculating tunnel responses.Moreover,a parametric study is conducted to evaluate the impact of key factors,including fault displacement,fault zone width,fault dip angle,earthquake frequency,rock conditions,tunnel lining stiffness,and tangential contact conditions,on tunnel responses.Compared with each effect alone,the combined effects of seismic waves and strike-slip faulting significantlychange the tunnel deformation and internal forces,leading to increased tunnel responses,especially within the fault zone and near the fault-rock interfaces.Depending on specificparameters,tunnel responses can be classifiedinto seismic-dominated,faulting-dominated,and seismic-faulting coupled responses on the basis of the relative contributions of each effect.The proposed analytical solution can be applied to quickly predict the longitudinal mechanical behaviour of tunnels under such combined effects in engineering applications. 展开更多
关键词 Strike-slip faulting Longitudinal tunnel response Analytical solution Seismic waves Wave transmissions and reflections
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Optimal combination of substrate supply amount coupled with nutrient solution management program for cucumber planting
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作者 Zhen Kang Zhaoxi Jiang +5 位作者 Zhaolong Liu Peng Wang Caihong Zhang Maozhou Yuan Mengqi Bai Xiaohui Hu 《Horticultural Plant Journal》 2026年第1期136-148,共13页
Substrate and nutrient supply are essential for vegetable cultivation in greenhouse.The strategies for plant nutrient supply vary depending on the cultivation methods or substrate dosages employed.With the development... Substrate and nutrient supply are essential for vegetable cultivation in greenhouse.The strategies for plant nutrient supply vary depending on the cultivation methods or substrate dosages employed.With the development of mechanization,wide-row spacing substrate cultivation became an optimize mode of the greenhouse cucumber cultivation,aligning with the trend of intelligent agriculture.To determine the optimal nutrient solution supply amount(NS)and supply frequency(SF)for promoting the integrated growth of cucumber under wide-row spacing substrate cultivation,we explored the effects of substrate supply amount(SS),NS,and SF on cucumber yield,quality,and element utilization efficiency.A five-level quadratic orthogonal rotation combination design with three experimental factors(NS,SF,and SS)was implemented for 23 coupling treatments over three growing seasons,including spring(2022S and 2023S)and autumn(2022A).The technique for order preference by similarity to ideal solution(TOPSIS)combining weights based on game theory was applied to construct cucumber comprehensive growth evaluation model.Single and two experimental factors analyses revealed significant effects of single factors and the coupling of NS-SS,NS-SF and SS-SF on the integrated growth of cucumber for all three growing seasons.For the NS-SF-SS combination,the optimal parameters for comprehensive cucumber growth were determined as follows:levels of^(-1).68 for NS,-0.7 for SF,and^(-1).682 for SS in 2022A;-0.43 for NS,-0.06 for SF,and 0.34 for SS in 2022S;0.3 for NS,-0.02 for SF,and 0.04 for SS in 2023S.Furthermore,for SS ranges of 2.00-3.01,3.01-4.50,4.50-5.99,5.99-7.00(L·plant^(-1)),the corresponding NS and SF intervals maximizing cucumber integrated growth in spring were:0.28-0.30(L·plant^(-1))and 6(times·d^(-1)),0.26-0.30(L·plant^(-1))and 6(times·d^(-1)),0.25-0.30(L·plant^(-1))and 6(times·d^(-1)),0.23-0.30(L·plant^(-1))and 6(times·d^(-1)),respectively.With the same SS,the corresponding NS and SF intervals that maximized cucumber integrated growth in autumn were:0.10(L·plant^(-1))and 8(times·d^(-1)),0.18(L·plant^(-1))and 7(times·d^(-1)),0.30(L·plant^(-1))and 6(times·d^(-1)),0.49(L·plant^(-1))and 5(times·d^(-1)),respectively.The results provide a theoretical basis for solution management,and further in-depth research on cucumber cultivation. 展开更多
关键词 Cucumis sativus L. Comprehensive growth Irrigation frequency Nutrient solution Substrate supply amount Wide row spacing
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Tailoring oxygen vacancies in Ni-doped In_(2)O_(3) for improved thin-film transistor stability and performance via solution processing
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作者 Fakhari Alam Sara Ajmal +3 位作者 Muhammad Asim Shahzad Ghulam Dastgeer Aamir Rasheed Gang He 《Journal of Semiconductors》 2026年第2期61-71,共11页
Doping in thin-film transistors(TFTs) plays a crucial role in tailoring material properties to enhance device performance, making them essential for advanced electronic applications. This study explores the synthesis ... Doping in thin-film transistors(TFTs) plays a crucial role in tailoring material properties to enhance device performance, making them essential for advanced electronic applications. This study explores the synthesis and characterization of TFTs fabricated using nickel(Ni)-doped indium oxide(In_(2)O_(3)) via a wet-chemical approach. The presented work investigates the effect of "Ni" incorporation in In_(2)O_(3) on the structural and electrical transport properties of In_(2)O_(3), revealing that higher "Ni" content decreases the oxygen vacancies, leading to a reduction in leakage current and a forward shift in threshold potential(V_(th)).Experimental findings reveal that Ni In O-based TFTs(with Ni = 0.5%) showcase enhanced electrical performance, achieving mobility of 7.54 cm^(2)/(V·s), an impressive ON/OFF current ratio of ~10^(7), a V_(th) of 6.26 V, reduced interfacial trap states(D_(it)) of 8.23 ×10^(12) cm^(-2) and enhanced biased stress stability. The efficacy of "Ni" incorporation is attributed to the upgraded Lewis acidity, stable Ni-O bond strength, and small ionic radius of Ni. Negative bias illumination stability(NBIS) measurements further indicate that device stability diminishes with shorter light wavelengths, likely due to the activation of oxygen vacancies. These findings validate the solution-processed techniques' potential for future large-scale, low-cost, energy-efficient, and high-performance electronics. 展开更多
关键词 thin-film transistors Ni-doped In_(2)O_(3) solution processing bias illumination stability
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In-situ stress solution theory for borehole overcoring technique incorporating time-dependent effect of stress relief and its applications
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作者 Daohong Xia Shengjun Miao +5 位作者 Lianjun Chen Yuan Li Zejing Liu Rongmin Zhang Pengjin Yang Pengcheng Li 《International Journal of Mining Science and Technology》 2026年第1期187-203,共17页
In-situ stress is a key parameter for underground mine design and rock stability analysis.The borehole overcoring technique is widely used for in-situ stress measurement,but the rheological recovery deformation of roc... In-situ stress is a key parameter for underground mine design and rock stability analysis.The borehole overcoring technique is widely used for in-situ stress measurement,but the rheological recovery deformation of rocks after stress relief introduces errors.To improve accuracy,this study proposes an in-situ stress solution theory that incorporates time-dependent stress relief effects.Triaxial stepwise loadingunloading rheological tests on granite and siltstone established quantitative relationships between instantaneous elastic recovery and viscoelastic recovery under different stress levels,confirming their impact on measurement accuracy.By integrating a dual-class elastic deformation recovery model,an improved in-situ stress solution theory was derived.Additionally,accounting for the nonlinear characteristics of rock masses,a determination method for time-dependent nonlinear mechanical parameters was proposed.Based on the CSIRO hollow inclusion strain cell,time-dependent strain correction equations and long-term confining pressure calibration equations were formulated.Finally,the proposed theory was successfully applied at one iron mine(736 m depth)in Xinjiang,China,and one coal mine(510 m depth)in Ningxia,China.Compared to classical theory,the calculated mean stress values showed accuracy improvements of 6.0%and 9.4%,respectively,validating the applicability and reliability of the proposed theory. 展开更多
关键词 In-situ stress solution theory Borehole overcoring technique Time-dependent effect of stress relief Viscoelastic recovery strain of rock In-situ stress measurement
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Multimodal fluorescent switch:pressure-induced emission and solution-induced optical anti-counterfeiting and logic gates
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作者 Jingtian Wang Xihan Yu +2 位作者 Kai Wang Guanjun Xiao Bo Zou 《Science Bulletin》 2026年第3期490-494,共5页
Multifunctional optical responsive materials have grown increasingly pivotal in addressingthe escalating demands of sensing,detection,and anti-counterfeiting applications[1,2].These materials exhibit distinct visible ... Multifunctional optical responsive materials have grown increasingly pivotal in addressingthe escalating demands of sensing,detection,and anti-counterfeiting applications[1,2].These materials exhibit distinct visible optical variations upon exposure to external stimuli,such as pressure,temperature,light,solvents,pH fluctuations,or mechanical force.Fluorescent sensing and anti-counterfeiting technologies leveraging these optical responses have emerged as highly promising solutions. 展开更多
关键词 sensing multifunctional optical responsive materials logic gates optical responsive materials multimodal fluorescent switch optical variations pressure induced emission solution induced optical anti counterfeiting
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Effect and mechanism of Ti−O solid solution layer on interfacial bonding strength of cold roll bonded titanium/stainless steel laminated composite plate
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作者 Zhi-yan YANG Xue-feng LIU +1 位作者 Hong-ting CHEN Xin MA 《Transactions of Nonferrous Metals Society of China》 2026年第1期171-182,共12页
Titanium plates with a Ti−O solid solution surface-hardened layer were cold roll-bonded with 304 stainless steel plates with high work hardening rates.The evolution and mechanisms affecting the interfacial bonding str... Titanium plates with a Ti−O solid solution surface-hardened layer were cold roll-bonded with 304 stainless steel plates with high work hardening rates.The evolution and mechanisms affecting the interfacial bonding strength in titanium/stainless steel laminated composites were investigated.Results indicate that the hardened layer reduces the interfacial bonding strength from over 261 MPa to less than 204 MPa.During the cold roll-bonding process,the hardened layer fractures,leading to the formation of multi-scale cracks that are difficult for the stainless steel to fill.This not only hinders the development of an interlocking interface but also leads to the presence of numerous microcracks and hardened blocks along the nearly straight interface,consequently weakening the interfacial bonding strength.In metals with high work hardening rates,the conventional approach of enhancing interface interlocking and improving interfacial bonding strength by using a surface-hardened layer becomes less effective. 展开更多
关键词 titanium/stainless steel laminated composite plate Ti−O solid solution hardened layer interlocking interface formation mechanism interfacial bonding strength
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Solutions of three-body problem based on an equivalent system approach
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作者 Jing Tang Xing 《Acta Mechanica Sinica》 2026年第1期292-309,共18页
Generalised reduced masses with a set of equations governing the three relative motions between two of 3-bodies in their gravitational field are established,of which the dynamic characteristics of 3-body dynamics,fund... Generalised reduced masses with a set of equations governing the three relative motions between two of 3-bodies in their gravitational field are established,of which the dynamic characteristics of 3-body dynamics,fundamental bases of this paper,are revealed.Based on these findings,an equivalent system is developed,which is a 2-body system with its total mass,constant angular momentum,kinetic and potential energies same as the total ones of three relative motions,so that it can be solved using the well-known theory of the 2-body system.From the solution of an equivalent system with the revealed characteristics of three relative motions,the general theoretical solutions of the 3-body system are obtained in the curve-integration forms along the orbits in the imaged radial motion space.The possible periodical orbits with generalised Kepler’s law are presented.Following the description and mathematical demonstrations of the proposed methods,the examples including Euler’s/Lagrange’s problems,and a reported numerical one are solved to validate the proposed methods.The methods derived from the 3-body system are extended to N-body problems. 展开更多
关键词 Three-body problem Equivalent system with solutions Orbit-equation of a conic section Generalised reduced mass Chaotic motions Generalised Kepler’s law N-body problem
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Global Classical Solutions for One Dimensional Navier Stokes Equations
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作者 罗党 《Chinese Quarterly Journal of Mathematics》 CSCD 2000年第4期74-79,共6页
In this article the author considers Cauchy problem for one dimensional Navier Stokes equations and the global smooth resolvablity for classical solutions is obtained.
关键词 Navier Stokes equations Cauchy problem global classical solution
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GLOBAL EXISTENCE AND BLOW-UP PHENOMENA OF CLASSICAL SOLUTIONS FOR THE SYSTEM OF COMPRESSIBLE ADIABATIC FLOW THROUGH POROUS MEDIA
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作者 刘法贵 孔德兴 《应用数学和力学》 EI CSCD 北大核心 2004年第6期643-652,共10页
By means of maximum principle for nonlinear hyperbolic systems, the results given by HSIAO Ling and D. Serre was improved for Cauchy problem of compressible adiabatic flow through porous media, and a complete result o... By means of maximum principle for nonlinear hyperbolic systems, the results given by HSIAO Ling and D. Serre was improved for Cauchy problem of compressible adiabatic flow through porous media, and a complete result on the global existence and the blow-up phenomena of classical solutions of these systems. These results show that the dissipation is strong enough to preserve the smoothness of ‘small ’ solution. 展开更多
关键词 多孔介质 可压缩流体力学 方程组 经典解 整体存在性 破裂
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GLOBAL CLASSICAL SOLUTION TO THE CAUCHY PROBLEM OF THE 3-D COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH DENSITY-DEPENDENT VISCOSITY 被引量:4
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作者 叶嵎林 《Acta Mathematica Scientia》 SCIE CSCD 2016年第5期1419-1432,共14页
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
关键词 global existence classical solution compressible Navier-Stokes equations density-dependent viscosity VACUUM
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ON THE EXISTENCE OF LOCAL CLASSICAL SOLUTION FOR A CLASS OF ONE-DIMENSIONAL COMPRESSIBLE NON-NEWTONIAN FLUIDS 被引量:5
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作者 方莉 李自来 《Acta Mathematica Scientia》 SCIE CSCD 2015年第1期157-181,共25页
In this paper, the aim is to establish the local existence of classical solutions for a class of compressible non-Newtonian fluids with vacuum in one-dimensional bounded intervals, under the assumption that the data s... In this paper, the aim is to establish the local existence of classical solutions for a class of compressible non-Newtonian fluids with vacuum in one-dimensional bounded intervals, under the assumption that the data satisfies a natural compatibility condition. For the results, the initial density does not need to be bounded below away from zero. 展开更多
关键词 compressible non-Newtonian fluids VACUUM local classical solution
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GLOBAL EXISTENCE AND BLOW-UP PHENOMENA OF CLASSICAL SOLUTIONS FOR THE SYSTEM OF COMPRESSIBLE ADIABATIC FLOW THROUGH POROUS MEDIA 被引量:2
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作者 刘法贵 孔德兴 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2004年第6期703-713,共11页
By means of maximum principle for nonlinear hyperbolic systems, the results given by HSIAO Ling and D. Serre was improved for Cauchy problem of compressible adiabatic flow through porous media, and a complete result o... By means of maximum principle for nonlinear hyperbolic systems, the results given by HSIAO Ling and D. Serre was improved for Cauchy problem of compressible adiabatic flow through porous media, and a complete result on the global existence and the blow-up phenomena of classical solutions of these systems. These results show that the dissipation is strong enough to preserve the smoothness of ‘small ’ solution. 展开更多
关键词 porous media compressible adiabatic flow system of equations classical solution global existence BLOW-UP
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GLOBAL EXISTENCE OF CLASSICAL SOLUTION FOR A VISCOUS LIQUID-GAS TWO-PHASE MODEL WITH MASS-DEPENDENT VISCOSITY AND VACUUM 被引量:2
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作者 王振 张卉 《Acta Mathematica Scientia》 SCIE CSCD 2014年第1期39-52,共14页
In this work, we obtain the global existence and uniqueness of classical solu-tions to a viscous liquid-gas two-phase model with mass-dependent viscosity and vacuum in one dimension, where the initial vacuum is allowe... In this work, we obtain the global existence and uniqueness of classical solu-tions to a viscous liquid-gas two-phase model with mass-dependent viscosity and vacuum in one dimension, where the initial vacuum is allowed. We get the upper and lower bounds of gas and liquid masses n and m by the continuity methods which we use to study the compressible Navier-Stokes equations. 展开更多
关键词 viscous liquid-gas two-phase model global classical solution VACUUM mass-dependent viscosity
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GLOBAL CLASSICAL SOLUTIONS TO THE 3-D ISENTROPIC COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH GENERAL INITIAL ENERGY 被引量:2
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作者 张培欣 邓雪梅 赵俊宁 《Acta Mathematica Scientia》 SCIE CSCD 2012年第6期2141-2160,共20页
We establish the global existence and uniqueness of classical solutions to the Cauchy problem for the 3-D compressible Navier-Stokes equations under the assumption that the initial density ||po||L∞ is appropriate... We establish the global existence and uniqueness of classical solutions to the Cauchy problem for the 3-D compressible Navier-Stokes equations under the assumption that the initial density ||po||L∞ is appropriate small and 1 〈 γ 〈 6/5. Here the initial density could have vacuum and we do not require that the initial energy is small. 展开更多
关键词 compressible Navier-Stokes equations global classical solutions general initial energy
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BLOW-UP OF CLASSICAL SOLUTIONS TO THE COMPRESSIBLE MAGNETOHYDRODYNAMIC EQUATIONS WITH VACUUM 被引量:1
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作者 朱圣国 《Acta Mathematica Scientia》 SCIE CSCD 2016年第1期220-232,共13页
In this paper, we consider the formation of singularity for the classical solutions to compressible MHD equations without thermal conductivity or infinity electric conductivity when the initial data contains vacuum. W... In this paper, we consider the formation of singularity for the classical solutions to compressible MHD equations without thermal conductivity or infinity electric conductivity when the initial data contains vacuum. We show that the life span of any smooth solution will not be extended to ∞, if the initial vacuum only appears in some local domain and the magnetic field vanishes on the interface that separates the vacuum and non-vacuum state, regardless the size of the initial data or the far field state. 展开更多
关键词 MHD infinity electric conductivity classical solutions VACUUM BLOW-UP
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A NECESSARY AND SUFFICIENT CONDITION FOR GLOBAL EXISTENCE OF CLASSICAL SOLUTIONS TO CAUCHY PROBLEM OF QUASILINEAR HYPERBOLIC SYSTEMS IN DIAGONAL FORM 被引量:1
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作者 郑永树 刘法贵 《Acta Mathematica Scientia》 SCIE CSCD 2000年第4期571-576,共6页
This article considers Cauchy problem for quasilinear hyperbolic systems in diagonal form. A necessary and sufficient condition in guaranteeing that Cauchy problem admits a unique global classical solution on t ≥ 0 i... This article considers Cauchy problem for quasilinear hyperbolic systems in diagonal form. A necessary and sufficient condition in guaranteeing that Cauchy problem admits a unique global classical solution on t ≥ 0 is obtained, and a sharp estimate of the life span for the classical solution is given. 展开更多
关键词 Cauchy problem global classical solution BLOW-UP life s
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