A Class Of Singular Semilinear Reaction Diffusion Behavior Of The Cauchy Problem Solution

With the development of science and technology, people made a variety of solving problem for evolution equation. However, the vast majority of case, these problems can not explain in the formula cell, or have complex expressions. Therefore, we can only analyse their attitudes(qualitative) theoretically. As to different types of evolution equation (especially the nonlinear and coupled problem), the study of their solutions hasn't been halted, and has got many good results, and developed many effective approaches, such as compactness method, monotonous method, semi-group approach and method of compensation for compactness. But the rang of evolution equations is very broad and the specific characteristics of nonlinear equations is vary, and some attitudes of some class solutions can be got only on very specially conditions. Therefore, there are many results often only suitable for a specific category of the physical models and a specific equations. As to the singular semi-linear evolution system in this article, we mainly used the semi-group approach to discuss them. In addition, we have used a number of commonly used integral inequality, such as Jensen inequality, Holder inequality, and some important principles and theory, such as the Lebesgue dominated convergence theorem, Banach fixed-point theorem, Duhamel principle, folding principle. For the nonlinear system, we have got the existence and uniqueness of their solutions, and the estimate expression and Blow-up problem of their solution when the nonlinear items meet certain conditions. For the linear system ,we have got the set of their solution, and extended the results to the N-place system.