带调和势的非线性Schrdinger方程爆破解的L~2集中性质

本文讨论了带调和势的具有临界幂的非线性schrdinger方程,得到其爆破解在t→T(爆破时间) 的几个重要性质;在L2空间中强极限的不存在性;爆破点以及L2集中性质.     

二维空间上一类半线性波动方程的爆破问题

本文用类似于[1]中解决爆破问题的方法，对二维空间上一类半线性波动方程的初值问题证得了：当非线性项F（u）∈C2（R）和初值g（x）∈CO（R2）且满足一定条件时，初值问题不存在全局C2-解．     

一类非线性反应扩散方程在高维空间的爆破解

主要讨论了一类具有Dirichlet边界条件的非线性反应扩散方程在高维空间的爆破解.通过构造恰当的辅助函数和利用一阶微分不等式技术,给出了在高维空间下爆破解存在的充分条件以及爆破时刻的上下界.     

带调和势的临界非线性Schr(o)dinger方程的爆破解

讨论了带调和势的临界非线性Schr(o)dinger方程的Cauchy问题,它是描述著名的Bose-Einstein凝聚的模型.得到带调和势的临界非线性Schr(o)diager方程爆破解的爆破速率的下界估计.进而,还得到径向对称爆破解的L2-集中性质.     

一类耦合非线性Schroedinger方程组的集中现象

在二维空间中考虑了一类非线性Schroedinger方程组．在能量守恒及质量守恒的基础上，通过对解的极限行为的研究，建立了一系列解在原点的局部恒等式，得到了方程组的径向对称爆破解的集中性质．     

带调和势的非线性Schrdinger方程爆破解的L~2集中率

本文讨论了带调和势的具有临界幂的非线性Schrodinger方程,得到其爆破解在t→T(爆破时间)的L2集中率．     

带调和势的非线性Schrdinger方程爆破解的L~2集中率

本文讨论了带调和势的具有临界幂的非线性Schrodinger方程,得到其爆破解在t→T(爆破时间)的L2集中率．     

半空间上具耦合非线性边界扩散系统的爆破性质

考虑半空间上具耦合非线性边界条件的热方程组解的爆破估计. 给出了爆破速率的上界和下界估计, 得到了具零初值解的惟一性和非惟一性结果.     

一类具阻尼非线性波动方程的Cauchy问题

本文研究一类具阻尼非线性波动方程Cauchy问题整体广义解和整体古典解的存在唯一性,并用凸性方法给出解爆破的充分条件.     

一类高阶非线性波动方程解的存在性

研究一类高阶非线性波动方程的初边值问题 ,证明问题局部广义解的存在性、唯一性 ,并用凸性方法证明解爆破的充分条件 .     

关于非线性波动方程的爆破现象

通过引入一类“爆破因子K(u,ut）”,讨论了非线性波动方程分别具Newmann边界条件和Dirichlet边界条件时,混合问题对于常见的各种非线性情形及初值条件,解在有限时间内的爆破行为。     

A Finite Difference Scheme for Blow-Up Solutions of Nonlinear Wave Equations

<正>We consider a finite difference scheme for a nonlinear wave equation,whose solutions may lose their smoothness in finite time,i.e.,blow up in finite time.In order to numerically reproduce blow-up solutions,we propose a rule for a time-stepping, which is a variant of what was successfully used in the case of nonlinear parabolic equations.A numerical blow-up time is defined and is proved to converge,under a certain hypothesis,to the real blow-up time as the grid size tends to zero.     

Blow-up Sets to a Coupled Heat System

This paper deals with a heat system coupled via local and localized sources subject to null Dirichlet boundary conditions. In a previous paper of the authors, a complete result on the multiple blow-up rates was obtained. In the present paper, we continue to consider the blow-up sets to the system via a complete classification for the nonlinear parameters. That is the discussion on single point versus total blow-up of the solutions. It is mentioned that due to the influence of the localized sources, there is some substantial difficulty to be overcomed there to deal with the single point blow-up of the solutions.     

带有非线性边界条件的非线性抛物型方程组的爆破速率估计

In this paper, the estimate on blow-up rate of the following nonlinear parabolic system is considered: We will prove that there exist two positive constants such that: where l_1= l_(21)α／α_2 l_(22),r=α_1／α_2＞1,α_1≤α_2＜0.     

耦合热方程组解的多重 Blow-up 速率

This paper deals with a heat system coupled via local and localized sources subject to null Dirichlet boundary conditions. Based on a complete classification for all the four nonlinear parameters, we establish multiple blow-up rates for the system under various dominations. We also determine uniform blow-up profiles for the three cases where localized source couplings dominate the system.     

Blow-up for a weakly dissipative modified two-component Camassa–Holm system

In this paper, we study the Cauchy problem of a weakly dissipative modified two-component Camassa–Holm (MCH2) system. We first derive the precise blow-up scenario and then give several criteria guaranteeing the blow-up of the solutions. We finally discuss the blow-up rate of the blowing-up solutions.