Analysis Of Several Kinds About Optimal Control For Population Systems With Diffusion And Age-structure In A Polluted Environment

With the rapid development of science and technology in today's society,while mankind enjoys the convenience brought by high technology,it is also accompanied by human damage to the living environment of various organisms.For example,during the development of industry,the discharge of sewage,waste gas,and industrial waste caused the appearance of haze and severely damaged the living environment of human beings.On the one hand,the destruction of the living environment harms the survival of various organisms to a certain extent.Therefore,the study of organisms in polluted environments is particularly important.On the other hand,due to the activity of the organism,it is also important to consider the diffusion factor in the model for studying the organism in a polluted environment.Considering the population diffusion and the impact of random environmental changes on the population,several new types of biological population models with age structure under environmental pollution were established,and the existence and uniqueness of the model solution and the corresponding optimal harvest control issues were studied accordingly.This article mainly divides into five chapters to study the optimal control of the population with diffusion and age structure in the polluted environment.The specific arrangement about this paper is following:The first chapter is the introduction of this paper,which mainly introduces the research background and research significance of this paper in this field,and gives a detailed introduction to the research status of biological populations in a polluted environment,and gives the main content of this paper.The second chapter is some preliminaries of this paper,some basic definitions related to this thesis is gaved,and lists the relevant lemmas and related theorems needed in this thesis.The third chapter studies the single population model with diffusion and age-structure in a polluted environment in two parts: the first part models a single population with diffusion and age-structure in a polluted environment,and the existence and uniqueness of the solution of the model were proved by the Banach fixed point theory,then,the corresponding optimal harvesting problem was studied.In the second part,considering the influence of environmental randomness on population,a new random single population model with diffusion and age-structure in polluted environment is established,and the existence and uniqueness of the solution of the model is derived.The fourth chapter mainly establishes and studies the two populations with diffusion and age-structure in a polluted environment,analyzes the optimal control problems of a class of population models with diffusion and age-structure in a polluted environment,and promotes the content of the first part of the third chapter.In this part,the existence and uniqueness ofthe solution of the competitive population model are proved through the Banach fixed point theory,and the corresponding optimal harvesting control problem is studied.The fifth chapter is the main work and conclusion of this paper,and the future work is prospected.In the future,it is worth thinking about the study of a multi-group dynamic system with diffusion and age-structure in a polluted environment.