Exponential Stability Of Traveling Waves Of Two Kinds Of Reaction-diffusion Models

The theory of traveling wave solutions of parabolic differential equations or system is one of the fastest developing areas of modern mathematics. Traveling wave solutions are solutions of special type of differential equations or system. Its wave profile is in-variant with respect to space under transition processes. Because it is largely applied in physics,chemistry,biology,epidemiology and other areas. so the study of the exis-tence,stability and other properties of traveling wave fronts has very important sense. This thesis is concerned with the stability of traveling wave fronts of two kinds of reaction-diffusion models.The second chapter is concerned with the stability of traveling waves fronts of a mouostable reaction-diffusion epidemic system with delay. When the initial perturbation around the traveling waves decays exponentially as.r→—∞,but can be arbitrarily large in other locations, the existence and comparison theorems of solutions in weighted space of corresponding Cauchy problem are first established for the system on R by appealing to the theories of analytic semigroup and abstract functional differential equations. then the methods of weighted-energy method combining comparison principle are applied to solve the stability of monostable fronts of delayed reaction-diffusion systems with monotonicity in some appropriate exponential weighted space and prove the global exponential stability of monostable fronts under the so-called large initial perturbation.The third chapter is concerned with the stability of traveling waves fronts of a popu-lation dynamic model on 2D lattice. The same method, that is, weighted-energy method combining with comparison principle is used to prove the exponential stability of traveling wave fronts of the model. The result of this stability requires that the initial perturbation around the wave is also satisfies decays exponentially as x→—∞, but can be arbitrarily large in other locations.