The Existence Of Wave Solution Of Two Reaction Diffusion Equations

Lattice dynamical system is the system of infinite number of ordinary differential e-quations or difference equations. It plays an extensive role in the artificial neural network, chemical reaction theory, image processing, materials science, electrical engineering, biology and other fields.In recent years, many experts and scholars pay attention to the theory and application of lattice dynamical system. Especially, the wave solutions of lattice discrete dynamical system have obtained some research results, these results mainly concentrated on researching1+1-dimensional space, for higher dimensional case it has no results.In this paper, we give the definition of three periodic wave solutions and their associated lemmas.the existence of the wave solution of a reaction diffusion equations with polynomial can be transformed into the problem of the existence of solution of partial difference equation. In the last chapter, we give two kinds of reaction diffusion equations and prove the existence of the solution, especially for which with a BangBang control, we obtained its (2,2)and (2,3)-periodic solutions...