The Existence And Uniqueness Of Two Biomathematical Models

With the rapid development of science and technology,people have higher requirements for the prevention and treatment of diseases.Among them,many bio-mathematical models can well fit the mechanism of disease development.In this paper,two mathematical models with biological backgrounds are studied,and the existence and uniqueness of their local solutions and global solutions are strictly proved.The first research is about the model and mechanism of retinal oxygen distribution and cerebral hemoglobin action.Most retinal blindness is a disease related to vascular components,and interrupting the oxygen supply in the retina is a key factor in the development of the disease.It is of great practical significance to study the distribution of retinal oxygen and the model of brain hemoglobin.The second one is about the glioblastoma model.The in-depth study of the glioblastoma model is conducive to the use of different protocols for resection and chemotherapy,which can provide patients with a maximum survival time treatment combination.The first chapter of this paper mainly expounds the research status,symbols and lemma of these two biological mathematical models.The second chapter studies a mathematical model of the interaction between retinal oxygen distribution and brain hemoglobin.The model is a coupled system of partial differential equations.In this paper,we discuss the mass concentration of oxygen,the concentration of brain hemoglobin,the mass concentration of brain hemoglobin and histidine,and the mathematical model of the concentration of hemoglobin and oxygen,by using Banach fixed point theorem and parabolic equation.The estimation proves the existence and uniqueness of the overall solution of the model.The third part is about the mathematical model of a glioblastoma.The model contains ordinary differential equations and hyperbolic equations that are coupled to each other.Firstly,the free boundary problem is transformed into a fixed boundary problem.Then the Banach fixed point theorem and estimation are used to prove the existence and uniqueness of the global solution of the fixed boundary problem.Finally,the existence of the original model solution is obtained.