复变量热传导方程的动力系统

熊辉; 杨光

doi:10.3879/j.issn.1000-0887.2014.09.011

复变量热传导方程的动力系统

doi: 10.3879/j.issn.1000-0887.2014.09.011

熊辉,
杨光

东莞理工学院数学教研室, 广东东莞 523808

基金项目: 国家自然科学基金(11271069)

详细信息

作者简介:
熊辉(1978—), 副教授, 博士(通讯作者. E-mail: xhui@163.com).

中图分类号: O193; O175.26
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出版历程
- 收稿日期: 2013-12-25
- 修回日期: 2014-01-13
- 刊出日期: 2014-09-15

Dynamics of a Complex-Valued Heat Equation

Department of Mathematics, Dongguan University of Technology,

Funds: The National Natural Science Foundation of China(11271069)

摘要

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.
- 复变量热方程 /
- 全局解 /
- 淬火点
Abstract: 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.
- complex-valued heat equation /
- global solution /
- quenching point

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参考文献(14)

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