Bifurcation Analysis For A Free Boundary Problem Modeling Growth Of Angiogenesis Tumor

In this thesis,we investigate the bifurcation phenomenon for a free boundary problem modeling growth of tumor with angiogenesis and inhibitor,namely,the existence of the radially symmetric stationary solutions and non-radially symmetric stationary solutions.This thesis is divided into three chapters.In chapter 1,we introduce some known research related on our problems,and our main results.In chapter 2.we study a free boundary problem modeling growth of angiogenesis tumor with inhibiter,namely:(?)where Ω is the tumor domain,σ,β,p denote the concentration of nutrient,concentraion of inhibitor and internal pressure within tumor,respectively.k is the mean curvature and n is the outward normal on free boundary(?)Ω.μ is a tumor aggressiveness parameter,σ is the threshold value of nutrient concentration,σ represents the external nutrient concentration,β represents the external inhibitor concentration.σ,σ,β,λ,α,γ are positive constants and satisfy α/α+1σ-σ-τβ>0.We obtain the existence of the radially symmetric solution of the problem for all y,>0,then prove that there exist a positive integer m**and a sequence of μm,such that for each even μm(m>m**),there exist a branch of symmetry-breaking solutions bifurcating from the above radially symmetric solution.We also prove that μm is increasing with respect to the supply of inhibitor βIn chapter 3,we study a free boundary problem modeling growth of angiogenesis tumor with inhibiter,namely:(?)where 7 is the surface tension coefficient.The meaniing of each paramet.er is the same as that of the second chapter.For μ(α/α+1σ-σ)-vβ>0,We obtain the existence of the radially symmetric solution of the problem for all 7>0.then prove that there exist a positive integer m**and a sequence of γm;such that for each even γm(m>m**),there exist a branch of symmetry-breaking solutions bifurcating from the above radially symmetric solution.