理想磁流体动力学方程组经典解的破裂

本文给出了理想磁流体动力学方程组的经典解在初始扰动适当大的情况下破裂的结果.文[1]证明了描述多方理想可压缩气体运动的欧拉系统的经典解在初始扰动适当大的情况下破裂的结果.本文将利用和文[1]相似的方法证明所得定理.     

一维可压粘性气体粘性激波的渐近稳定性

本文讨论一维粘性热传导多方气体粘性激波的渐近稳定性,如果初始扰动以及δ=|u+-u-|适当的小,则解在最大模的意义下趋于粘性激波.     

一维可压粘性气体粘性激波的渐近稳定性

本文讨论一维粘性热传导多方气体粘性激波的渐近稳定性,如果初始扰动以及δ=|u+-u-|适当的小,则解在最大模的意义下趋于粘性激波.     

一类流行病数学模型解的研究

该文讨论了一类非线性抛物型方程组解的性质，利用微分方程上、下解方法证明了初值适当小时，方程存在整体解；初值适当大时，解在有限时间上爆破，推广了文献[1]的结果．     

具有年龄结构的Lotka-Volterra竞争系统行波解的稳定性

主要研究了一类具有年龄结构的Lotka-Volterra竞争系统行波解的稳定性.在拟单调的情形下,利用解析半群理论和抽象泛函微分方程理论,首先建立起系统初值问题的解在R上的存在性和比较原理.然后基于加权能量法、比较原理和嵌入定理,建立起该系统在大初始扰动(即除去当x→-∞时在行波解附近的初始扰动是指数衰减的,在其他位置的初始扰动可以任意大)下,单稳大波速行波解的全局指数稳定性.研究结果表明,行波解作为系统的稳态解,通常决定着初值问题解的长时间渐近行为.其稳定性揭示了种间竞争的现象和结果能够被清晰地被观测到,而不受外界因素的干扰.     

KdV孤波解的稳定性

本文探讨了KdV孤波解在无穷小扰动下的稳定性,证明KdV孤波解在李亚普诺夫意义下是不稳定的.     

Boltzmann方程的L~1稳定性

本文研究在小初值情况下Boltzmann方程经典解的L1稳定性.借助于Toscani等人所给的估计,对硬位势和软位势作了讨论,完善了[2]中关于硬球模型的结果.     

抛物型方程解的一个性质

本文考虑无界区域上形如(1)的抛物型方程的解在|x|~2 t←∞时的增长性质,推广了[1]中对椭圆型方程的解得到的类似结果。     

非线性抛物型方程初边值问题解的Blow up性质

本文研究一类非线性抛物型方程具有非线性边界条件的初边值问题.利用抛物型方程最大值原理和凸性方法证明了该问题的解在有限时间内爆破.推广了文献[7-9]的结果.     

具有非线性阻尼和源项的弹性弦方程解的爆破（英文）

本文研究具有非线性阻尼和源项的弹性弦方程,基于文献[43]的思想,利用扰动的能量方法,研究其正初始能量解的爆破问题.     

A blow-up criterion for classical solutions to the compressible Navier-Stokes equations

In this paper, we obtain a blow-up criterion for classical solutions to the 3-D compressible Navier-Stokes equations just in terms of the gradient of the velocity, analogous to the Beal-Kato-Majda criterion for the ideal incompressible flow. In addition, the initial vacuum is allowed in our case.     

Global weak solutions and blow-up structure for the Degasperis-Procesi equation

In this paper we study several qualitative properties of the Degasperis-Procesi equation. We first established the precise blow-up rate and then determine the blow-up set of blow-up strong solutions to this equation for a large class of initial data. We finally prove the existence and uniqueness of global weak solutions to the equation provided the initial data satisfies appropriate conditions.     

On the finite time blow-up for filtration problems with nonlinear reaction

We present results for finite time blow-up for filtration problems with nonlinear reaction under appropriate assumptions on the nonlinearities and the initial data. In particular, we prove first finite time blow-up of solutions subject to sufficiently large initial data provided that the reaction term “overpowers” the nonlinear diffusion in a certain sense. Secondly, under related assumptions on the nonlinearities, we show that initial data above positive stationary state solutions will always lead to finite time blow-up.     

三维不可压磁流体方程组的显式爆破解

该文构造了三维磁流体方程组的若干分离变量型和自相似型显式爆破解.     

A blow-up criterion for 3D compressible viscoelastic flow with large initial data

In this paper, we consider a Cauchy problem for the three-dimensional compressible viscoelastic flow with large initial data. We establish a blow-up criterion for the strong solutions in terms of the gradient of velocity only, which is similar to the Beale-Kato-Majda criterion for ideal incompressible flow (cf. Beale et al. (1984) [20]) and the blow-up criterion for the compressible Navier-Stokes equations (cf. Huang et al. (2011) [21]).     

On the blow-up of solutions of equations of hydrodynamic type under special boundary conditions

We use the nonlinear capacity method to prove the blow-up of solutions of initial-boundary value problems of hydrodynamic type in bounded domains. We present sufficient boundary conditions ensuring the blow-up of the solution of an equation that is globally solvable under the classical boundary conditions. We estimate the blow-up time of solutions under given initial conditions. Note that it is the first result concerning blow-up for one of the problems considered.     

Global existence of solutions to a parabolic–elliptic chemotaxis system with critical degenerate diffusion

This paper is devoted to the analysis of nonnegative solutions for a degenerate parabolic–elliptic Patlak–Keller–Segel system with critical nonlinear diffusion in a bounded domain with homogeneous Neumann boundary conditions. Our aim is to prove the existence of a global weak solution under a smallness condition on the mass of the initial data, thereby completing previous results on finite blow-up for large masses. Under some higher regularity condition on solutions, the uniqueness of solutions is proved by using a classical duality technique.     

Blow-up for hyperbolic systems in diagonal form

We prove a blow-up result for classical solutions of the Cauchy problem for a nonlinear hyperbolic system in one space dimension. The initial conditions are periodic and the system is supposed to be in diagonal form. We give an estimate of the lifespan of the classical solutions. Received May 2000     

带非局部源的退化奇异半线性抛物方程的爆破

本文研究带齐次Dirichlet边界条件的非局部退化奇异半线性抛物方程ut-(xαux)x=∫0af(u)dx在(0,a)×(0,T)内正解的爆破性质,建立了古典解的局部存在性与唯一性.在适当的假设条件下,得到了正解的整体存在性与有限时刻爆破的结论.本文还证明了爆破点集是整个区域,这与局部源情形不同.进而,对于特殊情形:f(u)=up,p>1及,f(u)=eu,精确地确定了爆破的速率.     

On Exact Controllability of Networks of Nonlinear Elastic Strings in 3-Dimensional Space

This paper concerns a system of nonlinear wave equations describing the vibrations of a 3-dimensional network of elastic strings.The authors derive the equations and appropriate nodal conditions,determine equilibrium solutions,and,by using the methods of quasilinear hyperbolic systems,prove that for tree networks the natural initial,boundary value problem has classical solutions existing in neighborhoods of the "stretched" equilibrium solutions.Then the local controllability of such networks near such equilibrium configurations in a certain specified time interval is proved.Finally,it is proved that,given two different equilibrium states satisfying certain conditions,it is possible to control the network from states in a small enough neighborhood of one equilibrium to any state in a suitable neighborhood of the second equilibrium over a suffciently large time interval.