Global Solutions For A Predator-prey Model With Cross-diffusion And A Stage Structure

In recent years, the study on population dynamics has become one of the impor-tant research topics in the dynamical systems. As an important branch of mathe-matical biology, the population dynamics has been widely studied and developed. This paper considers the existence and uniform boundedness of the global solutions for the following predator-prey model with stage-structure and cross-diffusion in the form Applying the knowledge of partial differential equations and some mathematical thoughts to investigate the dynamical behaviors of the above model including the stability of nonnegative equilibrium and the properties of global solutions and so on. The energy estimate method, the extreme value principle, Gagliardo-Nirenberg inequality, Holder inequality, Young inequality, linearization method and the Lya-punov second method are used to obtain the main result in this paper.This paper is divided into six chapters:The first chapter mainly discusses the research background of global solutions of reaction-diffusion systems and the problems to be studied in this paper.The second chapter investigates the stability of nonnegative equilibria for the corresponding ODE model.The third chapter studies the local asymptotic stability of the positive equilib-rium of the above model with self-diffusion.The fourth chapter is concerned with the existence and uniform boundness of global solutions of the above model with cross-diffusion.The fifth chapter considers the global asymptotic stability of the positive equi-librium of the above model.The sixth chapter is some summaries.