非局部边界条件下的反应扩散方程的爆破解

Blow-up Solutions for Reaction Diffusion Equations with Nonlocal Boundary Conditions

研究Neumann非局部边界条件下具有梯度反应项的反应扩散方程的爆破解,利用构造适当的辅助函数和微分不等式技巧相结合的方法,证明了解的存在性,并得到了解发生爆破的条件以及爆破时间的上下界.

Considering the blow-up solution of reaction-diffusion equation with gradient reaction term under Neumann nonlocal boundary conditions,by using the method of constructing proper auxiliary function and the technique of differential inequality,the existence of the solution was proved,meanwhile,the upper and lower bounds on blow-up time when blow-up occurs were obtained.