Existence And Application Of Traveling Wavefronts For Several Types Of Reaction Diffusion Systems

In this thesis, we have disscussed the existence of traveling wavefronts forseveral general reaction systems with nonlinear diffusion and their applications, wegot sufficient conditions for the existence of traveling wavefronts.In chapter 1, we briefly introduce the background and meaningful of theproblems investigated in this thesis and give prelimilaries.In chapter 2, we investigate the existence of traveling fronts for a general reactionsystem with nonlinear symmetrical diffusion. As an application we employ theobtained results to show the existence of traveling fronts for a specific reaction-diffusion system in section 3.Chapter 3 is devoted to the study of traveling fronts for the Volume-fillingChemotaxis model with general kinetics. The obtained results can easily solve theproblems investigated in some related references. We also apply the obtained results todetect the existence of traveling wave solutions for two specific models.In chapter 4, we investigate the existence of traveling fronts for a partialdifferential equation with time delay. We show that for any wave speed in thenondelay problem, the traveling front can persist under the introduction of small delay.As an application we prove the existence of traveling front solutions of the diffusiveNicholson's blowflies equation.