Research On A Class Of Nonlinear Population Diffusion Models

In biomathematics,the dynamic character of population model has become an important content,many mathematicians and biologists have paid much attention to the study of population model with diffusion term.Reaction-diffusion equation is one of the basic equation describing physical movements,with the deepening of the research on reaction diffusion equations,it was found that the problem involved covers many subjects such as chemistry,physics,medicine and biology,and so has a strong application background and practical significance.This paper studies a class of nonlinear population diffusion model,that is,the model contains diffusion terms.The main work is to study the approximate solution of the population diffusion model,including the following aspects:In chapter one,we describe the research background of the topic,briefly introduces the research status of population model and the main work of this paper.In chapter two,we introduce some basic definitions and theorems,and related to the diffusion equation.In chapter three,we consider the situation that the population only changes with time or the diffusion coefficient is very small.The original nonlinear diffusion equation is simplified into a Logistic model with a harvest function.The improved model for different harvest functions and their exact solutions are used.The principle of least squares method and Matlab software perform are used in parameter estimation and curve fitting,and the improved model is used for the prediction of Chinese population.The effect is better than the existing results.In chapter four,we study the approximate solution of the population diffusion model with time and location.Based on the relevant properties and conclusions of the diffusion equation solution,the non-steady-state solution form of the model is constructed,and the existence of the approximate solution is proved by the Banach compression mapping theorem.In chapter five,we summarize the main work and conclusions of this paper and point out the future research direction of this topic.