具有空变系数和吸收项的抛物方程解的爆破分析

Blow-up analysis of solutions to a parabolic equation with space-dependent coefficients and inner absorption terms

研究了一类高维非局部抛物方程解的爆破现象.运用微分不等式技巧,得到了高维空间上非线性边界条件下具有空变系数和吸收项的抛物方程全局解的条件.进一步,通过构造能量表达式,运用Sobolev不等式和其他微分不等式技巧,推出了当爆破发生时解的爆破时间上界和下界估计.

Blow-up phenomena of solutions to nonlocal parabolic equation in high dimensional spaces are studied.By using a differential technique,the sufficient conditions for the global existence for the parabolic equation with space-dependent coefficients and inner absorption terms under nonlinear boundary conditions in high spaces are obtained.Furthermore,bound estimates of blow up time including an upper bound and a lower bound are derived by formulating energy expressions and using Sobolev inequalities and other differential methods when the blowup occurred.