| 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 |
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| 引用本文： | 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(A辑),2005,25(6):881-889. |
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| 作者姓名： | 陈友朋 谢春红 |
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| 作者单位： | [1]南京师范大学数学与计算机科学学院,南京210097 [2]盐城师范学院数学系,盐城224002 [3]南京大学数学系,南京210093 |
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| 基金项目： | 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 |
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| 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。
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| 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 |
| 文章编号： | 1003-3998(2005)06-881-09 |
| 收稿时间： | 2003-08-07 |
| 修稿时间： | 2004-06-02 |
Global Existence and Nonexistence for a Nonlinear Parabolic Equation with a Nonlinear Boundary Condition |
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| CHEN You-Peng,XIE Chun-Hong.Global Existence and Nonexistence for a Nonlinear Parabolic Equation with a Nonlinear Boundary Condition[J].Acta Mathematica Scientia,2005,25(6):881-889. |
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| Authors: | CHEN You-Peng XIE Chun-Hong |
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| Institution: | 1Department of Mathematics, Nanjing Normal University, Nanjing 210097;2Department of Mathematics, Yancheng Normal Institute, Yancheng 224.002;3Department of Mathematics, Nanjing University, Nanjing 210093 |
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| 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. |
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| Keywords: | Nonlinear parabolic equation Nonlinear boundary condition Global existence Finite time blow-up Upper and lower solutions |
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