Doubly Degenerate Parabolic Equation with Nonlinear Inner and Boundary Sources

一类具有非线性内部源和边界流的双重退化抛物型方程

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摘要 This paper deals with blow-up criterion for a doubly degenerate parabolic equation of the form （u^n）t = （｜ux｜^m-1ux）x ＋ u^p in （0, 1） × （0,T） subject to nonlinear boundary source （｜ux｜^m-1ux）（1,t） = u^q（1,t）, （｜ux｜^m-1ux）（0,t） = O, and positive initial data u（x,0） = uo（x）, where the parameters va, n, p, q 〉0. It is proved that the problem possesses global solutions if and only if p ≤ n and q〈min {n,m（n＋1）/m＋1}. This paper deals with blow-up criterion for a doubly degenerate parabolic equation of the form （u^n）t = （｜ux｜^m-1ux）x ＋ u^p in （0, 1） × （0,T） subject to nonlinear boundary source （｜ux｜^m-1ux）（1,t） = u^q（1,t）, （｜ux｜^m-1ux）（0,t） = O, and positive initial data u（x,0） = uo（x）, where the parameters va, n, p, q 〉0. It is proved that the problem possesses global solutions if and only if p ≤ n and q〈min {n,m（n＋1）/m＋1}.

作者姜朝欣

机构地区 Department of Applied Mathematics

出处《Northeastern Mathematical Journal》 CSCD 2007年第5期464-470,共7页 东北数学（英文版）

基金 The NNSF(10471013,10771024)of China.

关键词 doubly degenerate nonlinear parabolic equation BLOW-UP inner source boundary source global solution doubly degenerate, nonlinear parabolic equation, blow-up, inner source, boundary source, global solution

分类号 O175.2 [理学—基础数学]

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参考文献12

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共引文献2

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Northeastern Mathematical Journal

2007年第5期

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Doubly Degenerate Parabolic Equation with Nonlinear Inner and Boundary Sources

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