A Study On The Solution Of An Age-dependent Epidemic Dynamics With Nonlinear Diffusion

Population dynamic system is a model described the total number of a species (gener-ally assumed the species is people) constrained by conditions like time,space and so on.Theequation established corresponding to the model so called population equation could be asimulation to the change in law of the model. Population equations have a wide variety ofapplications in the census, the number of species statistics,especially in forecast the devel-opment trend of a species.The Asymptotic Behavior of a species can tell us the developmenttrend of this species.For the gradual solution of the equation research, development trendsof species in the forecast have relatively large, such as the application of some of its bi-ological phenomena in the interpretation and practical application is of great significance.Epidemic model is a population equation, which describes the Changes in the law of severalpopulations of the species with interaction.In this paper,we introduced the history and significance of the population equationsfirstly,and so as the epidemic equations.Then,we introduced a epidemic model and get anpartial differential equation from it.In the second chapter,after some prepare of some toolslike Sobolev Space we give the definition of weak solution about the equation mentionedbefore. In the third chapter we proved the existence of the approximate equations by FixedPoint Theorem.The get the existence of the solution of the main equations with Dirichletcondition by limitation.We proved the asymptotic behavior of the equations and uniquenessof solution by the estimates of various sobolev norm.