一类非局部退化反应扩散方程组解的存在性

Existence for a Class of Degenerate Reaction-diffusion Equations with Nonlocal Source

讨论了一类退化的具有非局部项的非线性反应扩散方程组解的存在性.首先利用了正则化方法证明正则问题解的存在性,进而证明了非线性反应扩散方程组的古典解的存在性;其次利用上下解方法来解决非线性反应扩散方程组解的整体存在,针对参数所满足的条件不同来构造不同结构的上解,从而得到了方程组解的整体存在条件.

The existence for a class of degenerate nonlinear reaction-diffusion equations with nonlocal source was investigated.Firstly,the existence of the solution of the regularization equations with the regularization method,and the existence of classical solution of the reaction-diffusion equations were proved.Secondly,by making use of super and low solution method,the global existence for the nonlinear reaction-diffusion equations was solved.Following the conditions for the parameter to construct different structures of the super solutions of the equations,the global existence conditions of the solutions of the equations were obtained.