The Existence And Uniqueness Of Solutions Of Singular Semilinear Evolution Equations And Asymptotic Behavior

In this paper,we prove the existence and unique of solution and existence of global solution by Semigroup theory for a class of the weakly coupling Singular Semilinear Reaction-diffusion Equations.That isWhereσ> 0, fi(x)(i= 1,2) are continuous, bounded and nonnegative.In this paper, we use Contraction Mapping Principle and Homogeneous principle to prove the existence and unique of solution and Iterative Principle to prove the Infinite growth.This paper arranges as that:In the first chapter, Singular Semilinear Evolution Equations is summarized, meanwhile, we draw conclusions.In the second chapter, we introduce basic knowledge including functional knowledge, inequality theory, and prove some lemmas.In the third chapter, we prove System of Equations have the unique solution in the strip [0,t)when pq>1.In the fourth chapter, we prove System of Equations have global solution when 0