GLOBAL EXISTENCE OF STRONG SOLUTIONS OF NAVIER-STOKES EQUATIONS WITH NON-NEWTONIAN POTENTIAL FOR ONE-DIMENSIONAL ISENTROPIC COMPRESSIBLE FLUIDS

The aims of this paper are to discuss global existence and uniqueness of strong solution for a class of isentropic compressible navier-Stokes equations with non-Newtonian in one-dimensional bounded intervals. We prove two global existence results on strong solutions of isentropic compressible Navier-Stokes equations. The first result shows only the existence. And the second one shows the existence and uniqueness result based on the first result, but the uniqueness requires some compatibility condition.     

一类非线性积分方程正解的存在唯一性

是人们关注的课题之一,1973年 P.J.Bushell 首先在[1]中用 Hilbert 投影距离证明了当 0<α<1时,方程(1)有唯一的正解;接着1975年 A.J.B.Botter 在文[2]中证明了在连续核 K(x,y)>0的情况下当 α=-1时方程(1)仍有唯一正解;此后便是讨论α>1的情况,1979年郭大钧在[3]中证明了若存在σ>0,使     

LOCAL EXISTENCE OF SOLUTION TO FREE BOUNDARY VALUE PROBLEM FOR COMPRESSIBLE NAVIER-STOKES EQUATIONS

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.     

一类两相Stefan问题的弱解的局部存在性

本文讨论一维情形下一类两相Ｓｔｅｆａｎ问题,证明了弱解的局部存在性。     

一维可压流体力学方程组整体经典解

本文研究了一维可压流体力学方程组的Cauchy问题,利用特征线法和分析的技巧,在一些合理的假设下,得到了Cauchy问题整体经典解存在的一个充分必要条件.     

A REMARK ON THE ATTRACTORS OF NON－NEWTONIAN FLUIDS

This paper corrects some mistakes in the proof of absorbing sets theorem of attractors of non-Newtonian fluids, and establishes again the existence of bounded absorbing sets.     

一类线性积分方程解的存在唯一性

在这篇文章内我们证明了一类线性积分方程存在唯一解．并给出解的表示式．它以Ｆｒｅｄｈｏｌｍ方程和Ｖｏｌｔｅｒｒａ方程为特殊情形．     

EXISTENCE AND UNIQUENESS OF THE SOLUTION FOR A CLASS OF NONLINEAR FRACTIONAL DIFFERENTIAL SYSTEM

In this paper we prove the existence and uniqueness of the solution for a class of nonlinear fractional differential system, and investigate the dependence of the solution on the orderαi.     

EXISTENCE OF POSITIVE SOLUTION FOR A CLASS OF QUASILINEAR ELLIPTIC EQUATION

In this paper, we investigates the existence of positive solutions for a class of quasilinear elliptic equations by using the topological degree argument.     

LOCAL CLASSICAL SOLUTION OF FREE BOUNDARY PROBLEM FOR A COUPLED SYSTEM

This paper considers a two-phase free boundary problem for coupled system including one parabolic equation and two elliptic equations. The problem comes from the discussion of a growth model of self-lnaintaining protocell in multidimensional case. The local classical solution of the problem with free boundary F : y = g(x,t) between two domains is being seeked. The local existence and uniqueness of the problem will be proved in multidimensional case.     

关于弱非线性、弱涨落的Boltzmann方程链的经典解的存在性问题

本文按照Grad~([6])指出的方法具体地证明了弱非线性、弱涨落的Boltzmann方程链的经典解的存在性.     

一维半导体流体动力学模型的局部有界解

本文讨论了能量方程是压力一密度关系的一维半导体流体动力学模型方程,通过把欧拉－泊松方程变成拟线性波动方程,利用拟线性波动方程的局部解存在性,得到一维半导体流体动力学模型的局部解,并且解是有界的。     

一类带阻尼项的拟线性双曲型方程

本文讨论了从细杆的振动中提出的一类带阻尼项的拟线性双曲型方程的初边值问题的解在唯一性，利用已有的线性结果及动点定理结合能量估计建立了解的存在唯一性。     

一类拟双线性型变分不等式解的存在性

本文引入和讨论了一类拟双线性型变分不等式解的存在性问题，其结果改进了文［４－６］中的相应结果．     

一类具积分项非线性梁方程整体解的存在性

讨论了一类在轴向载荷作用下,有限长粘弹性梁的非线性振动问题,用Galerkin方法证明了问题的整体强解和整体经典解的存在性.     

关于p－拉普拉斯方程径向解的一点注记

本文研究方程ｄｉｖ（｜ｕ｜ｐ－２ｕ）＋｜ｘ｜ｌ｜ｕ｜τ－１ｕ＝０，ｘ∈Ｂ的Ｄｉｒｉｃｈｌｅｔ边值问题ｕ｜Ｂ＝０的径向解。应用山路引理，我们将文［１］的结果（ｐ＝２时）推广到一般情形，证明上述问题有一非平凡的径向解。     

ON THE LOCAL WELL-POSEDNESS FOR THE DUMBBELL MODEL OF POLYMERIC FLUIDS

In this paper, we consider the local well-posedness of smooth solutions to a coupled microscopic-macroscopic model for polymeric fluid in general space dimension and with general initial data in Holder space.     

THE EXISTENCE AND UNIQUENESS OF SOLUTION FOR A CLASS OF STOCHASTIC FUNCTIONAL EQUAFIONS ON S.P.SPACE

We staxt in discussing a class of more general functional equations in tliis paper, andthe maill ainl is to establish the existence and uniquenes8 of solution of a class of stochasticfunctioual equations on stochastic processes space (called "S.P space" for sllort). The11 usingthe resuIt to son1e specia1 kil1ds ofordillary differential equation, stochastic differential (integral)equation (called "S.D.E." or "S.I.E." fOr short), a series of corollaries l1ave been derived. Someof then1 can b…     

共振下一类常微分方程组周期解的唯一存在性

设 X,Y 是 Banach 空间,其中范数不加区分地都记作‖·‖。首先我们给出 Hada-mard 大范围隐函数定理新的证明,这个证明比较初等,它并不涉及覆盖空间和提升等概念。定理1 (Hadamard)。设 T∶X→Y 是连续 Fréchet 可微映射,假定对一切 x∈X,T 的 Fréchet 微商 T′(x)都是 X 到 Y 上的线性同胚。令ζ(R)(?)(?)(1/‖[T′(x)]~(-1)‖),如果 integral from 0 to ∞ ζ(R)dR= ∞,那么 T 是 X 到 Y 上的同胚。