具有非局部源的p-Laplace方程解的爆破时间下界估计

摘要/Abstract

摘要：

该文考虑了三维空间中具有非局部源的p-Laplace方程分别在Dirichlet边界条件和Robin边界条件下解的爆破性质.通过构造辅助函数并利用微分不等式的技巧，得到了两种边界条件下方程解的爆破时间下界估计.另外，给出了方程解在L²-范数下不会发生爆破的充分条件.

关键词: p-Laplace方程, Dirichlet边界条件, Robin边界条件, 爆破, 爆破时间下界

Abstract:

In this paper, we consider an initial boundary value problem for a p-Laplacian equation under Dirichlet boundary condition or Robin boundary condition in three dimensional space. We use a differential inequality technique to determine a lower bound of blow-up time for the blow-up solution. In addition, we also give a sufficient condition which implies that blow-up does not occur.

Key words: p-Laplacian equation, Dirichlet boundary condition, Robin boundary condition, Blow up, Lower bound of blow-up time

中图分类号:

O175

孙宝燕. 具有非局部源的p-Laplace方程解的爆破时间下界估计[J]. 数学物理学报, 2018, 38(5): 911-923.

Baoyan Sun. Lower Bound of Blow-Up Time for a p-Laplacian Equation with Nonlocal Source[J]. Acta mathematica scientia,Series A, 2018, 38(5): 911-923.

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