Several Kinds Of Paxtial Differential Equations Related To Tumor Immunity

In recent years,the study of tumor models immunity has become an important research field.Fixed boundary is a commonly used model,and free boundary is a new model.Based on these models,tumor immunity is related to an important part of its own system,which has attracted the interest of experts and scholars.As this paper mainly considers the existence and uniqueness of tumor immunity systems with different boundaries,the main contents are as follows:In Chapter 1,We review the background and development of related to tumor immunity systems,briefly introduce the structure of this paper,and give some signs and common conclu-sions.In Chapter 2,We studied T cells inhibit the growth model of cancer cells.by introducing an appropriate threshold of T cell killing rate to cancer cells to investigate the asymptotic behavior and free boundary changes of cancer cells.In Chapter 3,We mainly analyze a bounded open domain??R²reaction diffusion model mathematically,which describes the spatial distribution and temporal evolution of cancer cells C,dendritic cells D,Interleukin I₁₂,cytotoxic T cells T₈,tumor growth factor T_?,regulatory cells T_rand helper T cells T₁.We use Leray-Schauder fixed point theorem to prove the existence of the solution under the homogeneous Neumann conditions.The uniqueness,the nonnegativity and the estimates for the solutions are also proved.In Chapter 4,We consider a reaction-diffusion model in a bounded open domain??R²,which describes vascular endothelial growth factor?VEGF?,endothelial cells and oxygen.We use parabolic theory to prove the existence of the solution in the function space W₄^2,1?Q?under the homogeneous Neumann conditions.Then we get the existence of nonnegative solutionIn Chapter 5,we summarize the context of this paper and introduce the prospect of future research.