四阶椭圆型方程奇异摄动问题的渐近解

本文考虑了四阶椭圆型偏微分方程奇异摄动边值问题,建立了解及其导数的能量估计,并用Lyuternik-Vishik方法构造了形式渐近解.最后利用能量估计我们得到了渐近展开式余项的界.     

一类非线性退化波动方程解的爆破

考虑了有界区域上一类非线性退化波动方程的初边值问题.通过改进Vitillaro,Li和Tsai的方法,建立了非正的初始能量以及正的初始能量下解的爆破结果.同时,还给出了解的生命跨度估计.     

从等离子体物理中提出的广义Korteweg—de Vries方程解的L^2一致稳定性

本文研究由等离子体物理提出的广义ＫｄＶ方程的解的Ｌ＾２一致稳定性，讨论了这种方程的初值问题，首先建立了几个与通常能量估计不同的整体估计，随后证明了解的Ｌ＾２一致稳定性。     

三次自催化模型的整体解

该文利用重要不等式及能量积分方法首先得到了解的初等的先验估计．然后利用线性半群的有关性质及精细计算得到了解的最大模估计，从而证明了两类三次自催化模型在Dirichlet边界条件下整体解的存在性，并进而证明了第一类模型的最大吸引子的存在性．     

含奇异势和记忆项的四阶抛物方程解的整体存在性与爆破

本文研究一类具有奇异势和记忆项的四阶抛物方程在有界域上的初边值问题.当初值在稳定集中,初始能量在正有界范围内,根据Faedo-Galerkin方法结合Hardy-Sobolev不等式得到了问题解的整体存在性并建立了能量泛函的衰减估计;当初始能量为负时,利用凸方法证明了问题的解在有限时刻爆破并估计了爆破时间上界,该上界依赖于初始能量;当初值位于不稳定集,初始能量有上界时,通过构造辅助泛函获得了一个与初始能量无关的爆破时间上界.     

一类具有非线性阻尼项和源项的波动方程整体解的不存在性

研究了一类含有非线性阻尼项和源项的波动方程的初边值问题.证明了当初始能量E(0)满足0E(0)d(d为一正常数)时,问题的整体解的不存在性并给出了解的生命跨度估计.     

带非线性阻尼项的三维可压缩欧拉方程组的整体解

研究了三维空间中带非线性阻尼项的可压缩欧拉方程组的初值问题.利用能量估计和傅立叶分析的方法,在初值是常状态附近的一个H~3∩L~1中的小扰动时获得了初值问题的解整体存在,并得到了解在大时间的L~2,L~∞衰减率分别为t~(-3/4),t~(-3/2),将线性阻尼的情形推广到了非线性阻尼的情形.     

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。     

一类强藕合抛物型方程组整体解的存在性及渐近性态

本文把半群理论与能量方法结合起来，证明了一类强藕合非线性抛物型方程组的初边值问题解的整体存在性，并给出了解的Ｗ^{（２，ｐ）}全局估计．     

三级营养食物链交错扩散模型的整体解

应用能量估计方法和Gagliardo-Nirenberg型不等式证明了带自扩散和交错扩散项的三级营养食物链模型在齐次Neumann边值条件下整体解的存在唯一性和一致有界性.     

一类半线性积分微分方程初值问题之整体解的存在性与唯一性

本文运用能量廷拓方法,讨论了一类描述有内部热耗散的杆中热传导问题的半线性积分微分方程初值问题之整体古典解的存在性,并附带证明了该问题之古典解的唯一性。     

Global existence and decay of solution for the nonisentropic Euler–Maxwell system with a nonconstant background density

In this paper, the Cauchy problem for the nonisentropic Euler–Maxwell system with a nonconstant background density is studied. The global existence of classical solution is constructed in three space dimensions provided the initial perturbation is sufficiently small. The proof is mainly based on classical energy estimate and the techniques of symmetrizer. And the time decay of the solution is also established by combining the decay estimate of the Green’s function with some time-weighted estimate.     

Stoxes方程初边值问题的Phragmen－Lindelof二择性原理

本文对非定常的Ｓｔｏｋｅｓ方程的初边值问题证明了Ｐｈｒａｇｍｅｎ－Ｌｉｎｄｅｌｏｆ二择性原理，即证明Ｓｔｏｋｅｓ流函数的能量，随着与带状区域有限端距离的增加必定或者按指数率增长或者按指数率衰减．对能量衰减情况建立了Ｓｔｏｋｅｓ流速度的最大模的点点估计．并提出求全能量上界的方法．     

Local existence of the solution to the initial‐boundary value problem in nonlinear thermomicroelasticity theory

We prove a theorem about local existence (in time) of the solution to the first initial‐boundary value problem for a nonlinear system of equation of the thermomicroelasticity theory. At first, we prove existence, uniqueness and regularity of the solution to this problem for the associated linearized system by using the method of semi‐group theory. Next, basing on this theorem, we prove an energy estimate for the solution to the linearized system by applying the method of Sobolev space. At the end, using the Banach fixed point theorem, we prove that the solution of our nonlinear problem exists and is unique. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the decay of solutions to the 2D Neumann exterior problem for the wave equation

We consider the exterior problem in the plane for the wave equation with a Neumann boundary condition and study the asymptotic behavior of the solution for large times. For possible application we are interested to show a decay estimate which does not involve weighted norms of the initial data. In the paper we prove such an estimate, by a combination of the estimate of the local energy decay and decay estimates for the free space solution.     

Existence,Uniqueness and Asymptotic Behavior for the Vlasov–Poisson System with Radiation Damping

We investigate the Cauchy problem for the Vlasov–Poisson system with radiation damping.By virtue of energy estimate and a refined velocity average lemma, we establish the global existence of nonnegative weak solution and asymptotic behavior under the condition that initial data have finite mass and energy. Furthermore, by building a Gronwall inequality about the distance between the Lagrangian flows associated to the weak solutions, we can prove the uniqueness of weak solution when the initial data have a higher order velocity moment.     

Global solution of the Cauchy problem in nonlinear thermodi.usion in solid body

We prove a theorem about global existence (in time) of the solution to the initial‐value problem for a nonlinear hyperbolic parabolic system of coupled partial differential equation of second order describing the process of thermodiffusion in solid body. The corresponding global existence theorems has been proved using the L^p ‐ L^q time decay estimates for the solution of the associated linearized problem. Next, we proved the energy estimate in the Sobolev space with constant independent of time. Such an energy estimate allows us to apply the standard (continuation argument and to continue the local solution to one de.ned for all t ∈ 〈0, ∞)).     

Beam evolution equation with variable coefficients

We investigate a initial‐boundary value problem for the nonlinear beam equation with variable coefficients on the action of a linear internal damping. We show the existence of a unique global weak solution and that the energy associated with this solution has a rate decay estimate. Besides, we prove the existence and uniqueness of non‐local strong solutions. Copyright © 2004 John Wiley & Sons, Ltd.     

On the asymptotic behaviour and stability of the solution for the Broadwell model of the Boltzmann equation in three dimensions

The initial value problem for the full Broadwell model, in gas kinetic theory, is investigated. By means of a fixed point theorem an upper estimate for the solution is derived, provided that the initial values satisfy suitable a priori conditions. Since this estimate is function of the time, the asymptotic behaviour of the global solution is determined.