具有时变系数和吸收项的非线性非局部反应扩散系统解的爆破

Blow-up of solutions to a nonlinear nonlocal reaction-diffusion system with time-dependent coefficients and inner absorption terms

研究了非线性边界条件下具有时变系数和吸收项的非线性非局部反应扩散系统解的全局存在性和爆破问题。采用Sobolev不等式及其他微分不等式方法,构造能量表达式,在一定条件下得到了其所满足的微分不等式,进而推出了解的全局存在性和爆破发生时解的爆破时间下界估计。

Global existence and blow-up of solutions to a nonlinear nonlocal reaction-diffusion system with time-dependent coefficients and inner absorption terms under nonlinear boundary conditions are studied.Energy expressions are formulated.By using the technique of Sobolev inequalities and other differential ones,the energy satisfying a differential inequality under certain conditions is deduced.Finally,the global existence and lower bound estimates of blow up time are obtained respectively.