带加权非局部源项半线性反应扩散方程组解的整体存在与爆破

Global Existence and Blow-up of Solutions to Reaction-diffusion System with a Weighted Nonlocal Source

研究一类带齐次Dirichlet边界条件,具加权非局部源项的半线性反应扩散方程组,用上下解方法,给出了该问题整体解存在与爆破的条件,并建立解在区域内部的一致爆破模式.

This paper deals with a semi-linear reaction-diffusion system with a weighted nonlocal source, subject to the null Dirichlet boundary condition. By using super-and sub-solution techniques, we first give the conditions for that the classical solution exists globally and blows up in finite time respectively. Finally, the uniform blow-up pro-files in the interior are presented.