Traveling Wave Fronts Of A Class Of Reaction-diffusion Systems

In this paper, we discuss the existence of traveling wave fronts of reaction-diffusion systems with retardation and anticipation. The paper include two chapters.In chapter1, we consider the existence of traveling wave fronts of reaction-diffusion systems with retardation and anticipation. where the reaction term satisfies the so-called quasimonotonieity condition.In sector2,Substituting u(x,t)=φ(x+ct),φ∈2(R, Rn),ξ=x+ct, c>0into (*),one has the following system of functional differential equations Dφ"(ξ)-cφ’(ξ)+fc(φξ,φξ)=0,ξ∈R So we discuss the existence of solutions of functional differential equations, replacing discuss the existence of traveling wave fronts of reaction-diffusion systems.By defining the upper and lower solution and constructing iteration equations,we have monotone iteration sequence converged to the solutions of functional differential equations.In chapter2,In order to apply the powerful theory of monotone dynamical sys-tems.we use the upper and lower solution method and monotone iteration technol-ogy,studying the existence of traveling wave fronts of reaction-diffusion systems with retardation and anticipation. where the reaction term satisfies the nonquasiinonotonicity condition.As a cost of this relaxation,we have to impose more restrictions on the upper and lower solutions employed as initial iteration,in order to prove the existence of traveling wave fronts of reaction-diffusion systems.