BLOW-UP PHENOMENA FOR A NONLOCAL QUASILINEAR PARABOLIC EQUATION WITH TIME-DEPENDENT COEFFICIENTS UNDER NONLINEAR BOUNDARY FLUX

被引：22

作者：

Liu, Zhiqing ^{[1
]}

Fang, Zhong Bo ^{[1
]}

机构：

[1] Ocean Univ China, Sch Math Sci, Qingdao 266100, Peoples R China

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B | 2016年 / 21卷 / 10期

关键词：

Nonlocal quasilinear parabolic equation; time-dependent coefficients; blow-up time; upper bound; lower bound;

D O I：

10.3934/dcdsb.2016113

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper deals with blow-up phenomena for an initial boundary value problem of a nonlocal quasilinear parabolic equation with time-dependent coefficients in a bounded star-shaped region under nonlinear boundary flux. Using the auxiliary function method and modified differential inequality technique, we establish some conditions on time-dependent coefficients and nonlinearities to guarantee that the solution u(x, t) exists globally or blows up at some finite time t*. Moreover, upper and lower bounds of t* are obtained under suitable measure in high-dimensional spaces. Finally, some application examples are presented.

引用

页码：3619 / 3635

页数：17

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