Double Free Boundary Problems For Two Kinds Of Parabolic Equations

Free boundary problems are widely used in physics,chemistry,biological population dy-namics.They also have certain mathematical theoretical research significance and research value.Classical methods and theories that deal with fixed boundary problems are can not be used for free boundary problems directly.Therefore,the research of free boundary problems is also difficult.In this paper,we mainly discuss a class of double free boundary problems with both localized source term and local source term,and a class of double free boundary problems for degenerate parabolic equations.Local existence and uniqueness of solutions,regularity,finite time blowup and global existence of solutions are considered.This paper consists of four parts.In chapter 1 we summarize some research background and results related to our problem,and introduce the main content of this paper briefly.In chap-ter 2,we discuss a class of double free boundary problems with both localized source term and local source term.By making use of Schauder fixed point theorem,L~pestimate,Schauder eati-mate,Sobolev embedding theorem and other analysis methods,we establish local existence and uniqueness of the solution,regularity of the solution.Next,comparison principle are used to deduce some conditions for finite time blowup and global existence.In chapter 3,by construct-ing the approximation problem and comparison principle,then with the help of some classical analysis methods,we prove the existence of the maximal solution and the conditions for finite time blowup and global existence.In chapter 4,we make some conclusions and expectiations about the relevant problems in the coming.