Dynamical Properties And Applications Of Reaction Equations With Heterogeneous Diffusion

In this thesis, we discuss the dynamical properties and applications for several reaction equations with heterogeneous diffusion.In chapter1, we briefly introduce the background and meaningful of the problems investigated in this thesis and give prelimilaries used in this thesis.In chapter2, we investigate the general reaction equation with driven diffusion term on the existence and uniqueness of positive solutions, the attractivity of positive periodic solutions and the global attractivity of steady states. Furthermore, we employ the obtained results to show the relevant dynamical properties for a specific reaction diffusion equation.Chapter3is devoted to the study of the existence and uniqueness of the positive solution persistance and stability of the positive solution and the desired revenue of population for a reaction equation with driven-diffusion. Finally, we give the relevant application and numerically verify the theoretical results.In chapter4, we investigate the existence and uniqueness of the steady state and the asymptotic behaviour of the stability solution for a competitive system. As an application we study the classical Lotka-Volterra model with the heterogeneous diffusion term and the numerical results are used to check the theoretical results.