FORMATION OF SINGULARITY FOR COMPRESSIBLE VISCOELASTICITY Dedicated to Professor Constantine M. Dafermos on the occasion of his 70th birthday

The formation of singularity and breakdown of classical solutions to the threedimensional compressible viscoelasticity and inviscid elasticity are considered.For the compressible inviscid elastic fluids,the finite-time formation of singularity in classical solutions is proved for certain initial data.For the compressible viscoelastic fluids,a criterion in term of the temporal integral of the velocity gradient is obtained for the breakdown of smooth solutions.     

ERROR ESTIMATION OF SPECTRAL-DIFFERENCE METHOD FOR COMPRESSIBLE FLUID FLOW IN THREE-DIMENSIONAL SPACE

This paper is devoted to a combined Fourier spectral-finite difference method for solving 3-dimensional, semi-periodic compressible fluid flow problem. The error estimation, as well as the convergence rate, is presented.     

LOCAL WELL-POSEDNESS TO THE CAUCHY PROBLEM OF THE 3-D COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH DENSITY-DEPENDENT VISCOSITY

In this article, we prove the local existence and uniqueness of the classical solution to the Cauchy problem of the 3-D compressible Navier-Stokes equations with large initial data and vacuum, if the shear viscosity μ is a positive constant and the bulk viscosity λ(ρ) = ρβwith β≥ 0. Note that the initial data can be arbitrarily large to contain vacuum states.     

LARGE－TIME BEHMIOR OF SOLUTIONS FOR THE SYSTEM OF COMPRESSIBLE ADIABATIC FLOW THROUGHPOROUS MEDIA

ＬＡＲＧＥ－ＴＩＭＥＢＥＨＭＩＯＲＯＦＳＯＬＵＴＩＯＮＳＦＯＲＴＨＥＳＹＳＴＥＭＯＦＣＯＭＰＲＥＳＳＩＢＬＥＡＤＩＡＢＡＴＩＣＦＬＯＷＴＨＲＯＵＧＨＰＯＲＯＵＳＭＥＤＩＡ￥ＸＩＡＯＬＩＮＧ（Ｌ．ＨＳＩＡＯ）Ｄ．ＳＥＲＲＥ（ＩｎｓｔｉｔｕｔｅｏｆＭａｔ...     

LARGE-TIME BEHAVIOR OF SOLUTIONS FOR THE SYSTEM OF COMPRESSIBLE ADIABATIC FLOW THROUGH POROUS MEDIA

Consider the system{vt-ux=0,ut+p(v,s)x=-αu,α>0,st=0,which can be used to model the adiabatic gas flow through porous media.Here v is specific volume,u denotes velocity,s stands for entropy,p denotes pressure with pv<0 for v>0.It is proved that the solutions of (1) tend to those of the following nonlinear parabolic equation time-asymptotically:{vt=-1/αp(v,s)xx;st=0,u=-1/αp(v,s)x.     

拟线性双曲组的经典解的奇性形成

This paper deals with the asymptotic behavior of the life-span of classical solutions to Cauchy problem for general first order quasilinear strictly hyperbolic systems in two independent variables with weaker decaying initial data, and obtains a blow-up result for C1 solution to Cauchy problem.     

FORMATION OF SINGULARITIES FOR A KIND OF QUASILINEAR NON－STRICTLY HYPERBOLIC SYSTEM

The author gets a blow-up result of C1 solution to the Cauchy problem for a first order quasilinear non-strictly hyperbolic system in one space dimension.     

ASYMPTOTIC BEHAVIOR OF SOLUTIONS TOWARD THE SUPERPOSITION OF CONTACT DISCONTINUITY AND SHOCK WAVE FOR COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH FREE BOUNDARY

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 wav...     

关于二阶常微分方程周期解的定理

本文研究非自治非线性二阶常微分方程存在周期解的充分条件．在满足本文定理的条件下，作者证明所研究的二阶方程在相空间中的Ｐｏｉｎｃａｒｅ映射是平面上有奇点的动力系统，从而证明原方程有周期解．这一结果全面推广已有的若干结论．     

ASYMPTOTIC BEHAVIOR OF SOLUTIONS TOWARD THE SUPERPOSITION OF CONTACT DISCONTINUITY AND SHOCK WAVE FOR COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH FREE BOUNDARY Dedicated to Professor Constantine M. Dafermos on the occasion of his 70th birthday

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.     

LARGE-TIME BEHAVIOR OF SOLUTIONS OF QUANTUM HYDRODYNAMIC MODEL FOR SEMICONDUCTORS

A one-dimensional quantum hydrodynamic model (or quantum Euler-Poisson system) for semiconductors with initial boundary conditions is considered for general pressure-density function. The existence and uniqueness of the classical solution of the corresponding steady-state quantum hydrodynamic equations is proved. Furthermore, the global existence of classical solution, when the initial datum is a perturbation of the steady-state solution, is obtained. This solution tends to the corresponding steady-state solution exponentially fast as the time tends to infinity.     

非定常概周期系统局部结构稳定的充要条件

本文给出：如果一致概周期函数ｆ（ｔ，ｘ）满足：ｉ）ｆ（ｔ，０）＝０；ｉｉ）Ｄｘｆ（ｔ，ｘ）在Ｒ×Ｄ上有界（Ｄ是Ｒｎ中含原点的一个区域）；ｉｉｉ）对ｔ一致成立，那么系统关于Ｂ１（所有满足ｉ），ｉｉ）的一致概周期函数全体所成之集按范数构成的赋范线性空间）在原点邻域局部结构稳定的充要条件是它的零解变分系统在Ｒ上具有指数型二分性．进而得到系统关于Ｂ１在原点邻域局部结构稳定是可继承的．并推出这类结构稳定的系统在Ｂ１的某子空间中是处处稠密的．