Theory of characterization and existence for entire solutions to reaction-diffusion equations in the multi-dimensional space.

反应扩散方程是一种被广泛接受的描述空间模式形成和传播的模型。本文对该方程进行了研究，以提供一个完整解的存在性理论和解的空间格局的表征。因此，我们从数学上证明了一类反应扩散方程新解的存在性和稳定性。

The reaction-diffusion equation is widely accepted as a model to describe pattern formations and propagations of some spatial pattern. In this research we study the equation in order to provide a new existence theory for entire solutions and a characterization of the spatial pattern of the solutions. In consequence we mathematically prove the existence and stability of new type of solutions to some class of reaction-diffusion equations.