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  

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

作　　者：赵元章[1] 马相如 Zhao Yuanzhang;Ma Xiangru(School of Mathematical Sciences,Ocean University of China,Shandong Qingdao 266100)

机构地区：[1]中国海洋大学数学科学学院,山东青岛266100

出　　处：《数学物理学报（A辑）》2018年第4期750-769,共20页Acta Mathematica Scientia

基　　金：山东省研究生创新计划项目(SDYY14127)~~

摘　　要：该文考虑了具有变扩散系数的反应-扩散方程Dirichlet初边值问题解的爆破现象.利用辅助函数法和修正微分不等式技巧,对变扩散系数和非线性项给出适当的条件,以保证解整体存在或有限时刻发生爆破,并在整体空间中(N≥1)导出了爆破时间的界.同时,给出几个应用举例.In this paper,blow-up phenomena for the Dirichlet initial boundary value problemof a reaction-diffusion equation with variant diffusion coefficient is considered.By virtue of theauxiliary function method and the modified differential inequality,we.established appropriateconditions on variant diffusion coeficient and nonlinearities to guarantee existence of globalsolution or blow-up solution at finite time.Moreover,lower bounds for the blow-up time of thesolution are derived in all dimensional spaces(N 2 1).In the meantime,several examples arepresented to illustrate applications of our results.

关 键 词：反应-扩散方程 变扩散系数 爆破时间的界 

分 类 号：O175.29[理学—数学]