Free Boundary Problem Modeling Tumour Cord With An Almost Periodic Supply Of Nutrients

This thesis concerns the existence,uniqueness and exponential stability of the almost periodic solution of the free boundary problem modeling tumour cord with an almost periodic supply of nutrients.The full text is divided into three chapters.In chapter 1,we introduce the related research on the considered problems and our main results.In chapter 2,we discuss the existence,uniqueness and exponential stability of the almost periodic solution of the free boundary problem modeling tumour cord with an almost periodic supply of nutrient in quasi-stationary case,in which we consider the following problem:where σ represents the concentration of nutrients in the tumor;Δr=?2/?r2+1/r ?/?r;a represents the radius of the inner boundary of the tumor;R(t)represents the outer boundary radius of the tumor;γ(t)represents the concentration of nutrients around the tumor,which is an almost periodic function;σ represents the threshold of nutrient concentration required for tumor cell to mitosis;R0 represents the initial condition.For this problem,using the fixed point theorem in cones,we prove the existence and uniqueness of the almost periodic solution.By using the Gronwall inequalities,we establish the exponential stability of the almost periodic solution.The results are illustrated by numerical simulation.In chapter 3,we discuss the free boundary problem modeling tumour cord with an almost periodic supply of nutrient and time delay in quasi-stationary case,namely:where τ represents the time of cell mitosis;φ(t)represents the initial condition.For this problem,we prove the existence and uniqueness of the almost periodic solution,and establish the exponential stability of the almost periodic solution.The results and the effect of time delay on tumor growth are illustrated by numerical simulations.