复变量热传导方程的动力系统  

Dynamics of a Complex-Valued Heat Equation

作　　者：熊辉[1] 杨光[1] 

机构地区：[1]东莞理工学院数学教研室,广东东莞523808

出　　处：《应用数学和力学》2014年第9期1055-1062,共8页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(11271069)~~

摘　　要：探讨一个复变量热方程的Cauchy问题,其中的非线性项是倒数型的.先提出一些全局解的存在性与不存在性的判定准则,然后采用解平面的不变子集的变换,证明了当初始值渐近于常数时,解是否会在无穷远处消失或在任意时间内全局存在,均依赖于初始值的渐近极限值.The Cauchy problem for a parabolic system which was derived from a complex-valued heat equation with inverse nonlinearity was studied. Some criteria for the global existence and quenching of the solutions were provided. Through transformation of the invariant subset of the solution plane, it was proved that, for the initial values which are asymptotically constants, whether the solution quenches at spatial infinity or exists globally at any time, depends on the asymptotic limits of the initial values.

关 键 词：复变量热方程 全局解 淬火点 

分 类 号：O193[理学—数学] O175.26[理学—基础数学]