一类非牛顿系统弱解的长时间性态

本文讨论一类非牛顿系统弱解的长时间性态,证明解在L2 范数下的衰减速率为(1 t)-n/4 达到和线性热方程一致.     

具非线性边界条件的非牛顿渗流方程弱解的局部存在性

利用能量方法,证明了一类具有Neumann边界条件的非牛顿渗流方程弱解的局部存在性.     

一类无界区域中的椭圆型系统非局部边值问题

本文讨论了一类在无界区域中的非线性椭圆系统的非局部边值问题。在适当的条件下,相对边值问题解的存在性及其比较定理作了研究。     

一类非牛顿流弱解的扰动

主要研究一类可压缩粘性非牛顿流方程弱解的扰动性质.在已知弱解存在的基础上,证明了选取适当范数时,沿着给定的时间序列,密度和速率的扰动趋于零.     

二维无界区域中不可压非牛顿流体力学方程组的整体吸引子

研究一类二维无界区域中的等热双极不可压粘性非牛顿流体力学方程组，通过证明和相应的解半群的紧性，得到整体吸引子的存在性。     

具非线性边界条件的非牛顿渗流方程整体弱解的存在唯一性

证明了一类具有非线性边值条件的非牛顿渗流方程解的存在和唯一性。     

一类非牛顿多方渗流方程弱解的Holder连续性

对一类非牛顿多方渗流方程，我们得到其非负弱解的Ｈｏｌｄｅｒ连续性，并且部分地解决了有关的问题。     

一类具有非齐次项对称双曲系统整体弱解的存在性

研究一类具有非齐次项的对称双曲系统Cauchy问题,用补偿紧性方法和最大值原理,得到其有界弱解的整体存在性结果.这一结果推广文献[7]中对称双曲系统到非齐次对称双曲系统.这样一类问题产生于弹性理论、磁流体动力学和石油再开采领域中,具有一定理论和应用价值.     

趋化NS系统弱解的全局存在性（英文）

本文主要研究趋化NS系统在2维的有界光滑领域Ω?R~2中.本文利用Galerkin方法证明了不可压缩的NS系统弱解的存在性.其次,利用一系列检验程序,证明了带有初边值条件的趋化NS系统弱解的局部存在性,进一步得到该系统弱解的全局存在性.     

一类非线性抛物方程弱解的L~2 衰减(英文)

本文研究了非线性抛物方程弱解的L2 衰减 ,证明了若u是非线性抛物方程的一个弱解 ,则u满足‖u‖L2 ≤C( 1 t) -n/ 4,其中C是常数且仅依赖于初始值u0 的范数 .     

The Alexandrov-Bakelman-Pucci Weak Maximum Principle for Fully Nonlinear Equations in Unbounded Domains

ABSTRACT

We obtain Alexandrov-Bakelman-Pucci type estimates for semicontinuous viscosity solutions of fully nonlinear elliptic inequalities in unbounded domains. Under suitable assumptions relating the geometry of the domain with structural conditions on the differential operator, we establish the validity of the weak maximum principle for solutions which are bounded from above. Two variants are also given, namely one for unbounded solutions in narrow domains and one for operators with possibly changing sign zero order coefficients in domains of small measure.     

On Some Elliptic Problems in Unbounded Domains

The author presents a method allowing to obtain existence of a solution for some elliptic problems set in unbounded domains, and shows exponential rate of convergence of the approximate solution toward the solution.     

Large Time Behavior of a Weak Solution for Non-Newtonian Flow

This paper concerns large time behavior of a regular weak solution for non-Newtonian flow equations. It is shown that the decay of the solution is of exponential type when the force term is equal to zero and the domain is bounded. Moreover, the ratio of the enstrophy over the energy has a limit as time tends to infinity, which is an eigenvalue of the Stokes operator.     

无界区域上含p-Laplacian的共振问题

本文利用变分方法研究如下边值问题的可解性:-△pu=μQ（x）|u|p-2u+f（x,u）,u∈D_0~1,p（Ω）,其中Ω是RN中的开集,1相似文献   

The Existence and Long-Time Behavior of Weak Solution to Bipolar Quantum Drift-Diffusion Model

The authors study the existence and long-time behavior of weak solutions to the bipolar transient quantum drift-diffusion model,a fourth order parabolic system.Using semi-discretization in time and entropy estimate,the authors get the global existence of nonnegative weak solutions to the one-dimensional model with nonnegative initial and homogenous Neumann(or periodic)boundary conditions.Furthermore,by a logarithmic Sobolev inequality,it is proved that the periodic weak solution exponentially approaches its mean value as time increases to infinity.     

R~2上一类非牛顿流体动力学方程组解的最优衰减率

本文利用Fourier分解方法讨论一类二维不可压缩非牛顿流体动力学方程组弱解的衰减性,证明了弱解在L~2范数下衰减率为(1+t)~(-1/2),和线性热传导方程解的衰减率一致,在此意义下本文的结果是最优的。     

Uniqueness of Solutions on the Whole Time Axis to the Navier-Stokes Equations in Unbounded Domains

We consider the uniqueness of bounded continuous L^{3, ∞}-solutions on the whole time axis to the Navier-Stokes equations in 3-dimensional unbounded domains. Here, L^{p, q} denotes the scale of Lorentz spaces. Thus far, uniqueness of such solutions to the Navier-Stokes equations in unbounded domain, roughly speaking, is known only for a small solution in BC(?; L^{3, ∞}) within the class of solutions which have sufficiently small L^∞(L^{3, ∞})-norm. In this paper, we discuss another type of uniqueness theorem for solutions in BC(?; L^{3, ∞}) using a smallness condition for one solution and a precompact range condition for the other one. The proof is based on the method of dual equations.