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 ? is the tumor domain,?,?,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(?)?.? is a tumor aggressiveness parameter,? is the threshold value of nutrient concentration,? represents the external nutrient concentration,? represents the external inhibitor concentration.?,?,?,?,?,? are positive constants and satisfy ?/?+1?-?-??>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 ?m,such that for each even ?m(m>m**),there exist a branch of symmetry-breaking solutions bifurcating from the above radially symmetric solution.We also prove that ?m is increasing with respect to the supply of inhibitor ?In 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 ?(?/?+1?-?)-v?>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 ?m;such that for each even ?m(m>m**),there exist a branch of symmetry-breaking solutions bifurcating from the above radially symmetric solution.