非局部抛物方程组解的一致爆破

Uniform Blow-up for Nonlocal Parabolic Systems

考虑一类带有齐次Dirichlet边界条件,反应项为非局部源项的半线性抛物方程组解的爆破性质.运用构造上、下解方法,给出该问题解在有限时刻爆破的充分条件;在此基础上得到解的2个分量同时爆破的必要条件和1个充分条件;最后建立了解的爆破速率.

This paper deals with the blow-up properties of solutions to semilinear parabolic system with nonlocal source, subject to null Dirichlet boundary conditions. Using the upperlower method, we establish the conditions for the finite blow-up of solution to the system. The necessary conditions and a sufficient condition under which two components blow-up simultaneously are obtained. At last, the blow-up rate estimations are established.