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

反应扩散方程被广泛接受为描述某些空间模式的形成和传播的模型。在这项研究中，我们研究的方程，以提供一个新的整体解的存在性理论和空间模式的解决方案的表征。在此基础上，我们从数学上证明了一类反应扩散方程新的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.