一类具有变扩散系数的非局部反应-扩散方程解的爆破分析

Abstract

Abstract: In this paper, blow-up phenomena for the Dirichlet initial boundary value problem of a reaction-diffusion equation with variant diffusion coefficient is considered. By virtue of the auxiliary function method and the modified differential inequality, we established appropriate conditions on variant diffusion coefficient and nonlinearities to guarantee existence of global solution or blow-up solution at finite time. Moreover, lower bounds for the blow-up time of the solution are derived in all dimensional spaces (N ≥ 1). In the meantime, several examples are presented to illustrate applications of our results.

Key words: Reaction-diffusion equation, Variant diffusion coefficient, Bounds for the blow-up time

CLC Number:

O175.29

Zhao Yuanzhang, Ma Xiangru. Blow-Up Analysis for a Nonlocal Reaction-Diffusion Equation with Variant Diffusion Coefficient[J].Acta mathematica scientia,Series A, 2018, 38(4): 750-769.

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References 27

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Blow-Up Analysis for a Nonlocal Reaction-Diffusion Equation with Variant Diffusion Coefficient

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