一类带非线性边界条件的非线性抛物方程的解的整体存在性

数学物理学报 ›› 2005, Vol. 25 ›› Issue (6): 881-889.

一类带非线性边界条件的非线性抛物方程的解的整体存在性

陈友朋, 谢春红

南京师范大学数学与计算机科学学院南京 210097 盐城师范学院数学系盐城 224002 南京大学数学系南京 210093

出版日期:2005-12-24 发布日期:2005-12-24
基金资助:
江苏省博士后科研资助计划(11107013152)和盐城师范学院自然科学基金资助

Global Existence and Nonexistence for a Nonlinear Parabolic Equation with a Nonlinear Boundary Condition

CHEN You-Peng, XIE Chun-Hong

Online:2005-12-24 Published:2005-12-24
Supported by:
江苏省博士后科研资助计划(11107013152)和盐城师范学院自然科学基金资助

摘要/Abstract

摘要：

该文考虑带非线性边界条件的非线性抛物方程的正整体解的存在性与非存在性。通过使用上下解技巧，得到了所有正解整体存在的充分必要条件。作者所构造的上下解具有相同的形式且计算简便。

关键词: 非线性抛物方程, 非线性边界条件, 整体存在性, 有限时刻爆破, 上下解

Abstract:

This paper deals with the existence and nonexistence of global positive solutions of the nonlinear parabolic equation with a nonlinear boundary condition. A necessary and sufficient condition in order that all positive solutions exist globally is obtained by using the technique of the upper and lower solutions, which have the same form and they are simple in the calculations.

Key words: Nonlinear parabolic equation, Nonlinear boundary condit ion, Global existence, Finite time blow up, Upper and lower solutions

中图分类号:

35K55

陈友朋, 谢春红. 一类带非线性边界条件的非线性抛物方程的解的整体存在性[J]. 数学物理学报, 2005, 25(6): 881-889.

CHEN You-Peng, XIE Chun-Hong. Global Existence and Nonexistence for a Nonlinear Parabolic Equation with a Nonlinear Boundary Condition[J]. Acta mathematica scientia,Series A, 2005, 25(6): 881-889.

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