关键词: 退化抛物型方程组, 非局部源,  , 一致爆破模式, 同时爆破

Abstract:

This paper deals with the blow-up properties of positive solutions to degenerate parabolic systems with nonlocal sources, subject to null Dirichlet boundary conditions. Under appropriate hypotheses, the authors establish the local existence of the solution and the finite time blow-up. Moreover, they obtain a necessary condition for which the two components of the solution blow up simultaneously, and then establish the uniform blow-up profiles in the interior.

Key words: Degenerate parabolic systems, Nonlocal sources, Uniform blow-up profiles,  Simultaneous blow-up