两类非线性发展方程组解的爆破和熄灭  

Blowing up and Dying out of the Solutions to Two Types of Nonlinear Systems of Evolution Equations

作　　者：王凡彬[1,2] 

机构地区：[1]四川省高等学校数值仿真重点实验室 [2]内江师范学院数学与信息科学学院,四川内江641112

出　　处：《重庆师范大学学报（自然科学版）》2008年第4期33-36,共4页Journal of Chongqing Normal University:Natural Science

基　　金：四川省教育厅重点科研项目(No.2004A173)

摘　　要：考虑一类非线性双曲抛物耦合方程组和一类非线性反应扩散方程组具有三类边界条件的初边值问题,讨论它们解的爆破与熄灭。首先在区域Ω上建立一个含参数t的积分,得到一个以t为变量的函数,然后用凸分析的方法对该函数进行分析。在分析过程中利用了自共轭椭圆算子的特征函数,Grenn第一、第二公式,Jensen不等式,Hlder不等式等方法。证明了当非线性项、初值函数满足一定的条件,方程组的解必在有限时间内爆破或熄灭,给出了其解爆破或熄灭的充分条件。给出的充分条件比较简洁,较之繁冗的充分条件,更易于实际应用。This paper considers the initial boundary value problems with three types of boundary conditions for a class systems of non- linear hyperbolic parabolic coupled equations and a class systems of nonlinear reaction-diffusion equations. It discusses how to blow up and die out of their solutions. At first, we establish an integral containing the parameter t in the region Ω, get a function that t is variable and then use convex analysis method for analysis of the function. In the analysis of reasoning, eigenfunction of elf-conjugate elliptic operator, Grenn formula, the second formula, Jensen inequality, Holder inequality and other methods are used. There when the non- linear term, the initial function meet certain conditions, equations solution blowing up and dying out in the limited time are proved, sufficient conditions of their solution to blow up and die out are given. The sufficient condition is relatively simple, compared with the multiplication of sufficient conditions, and is more easily practical application.

关 键 词：非线性发展方程组 初边值问题 解 爆破 熄灭 

分 类 号：O175.29[理学—数学] O175.9[理学—基础数学]