Properties Of Solutions For A Class Of Semilinear Fractional Reaction-diffusion Equations

In this paper,we study the global solution,long time asymptotic behavior and blow up of the semilinear fractional reaction-diffusion equation with homogeneous Dirichlet boundary.Firstly,we will give some equivalent definitions of fractional Laplace operators and some related concepts.Using the Caffarelli-Silvestre extension method to transform the nonlocal problem into a variable local problem.Combing Gal(?)rkin method,we can get the existence of solution,and utilize some inequalities to get long time asymptotic behavior of global solutions.Lastly we use convex method to prove the blasting criterion of the equation.Firstly,we give the fractional reaction diffusion equations’ development background and research significance in the first chapter.In order to make it easier for readers to read,in the second chapter we list some basic concepts and inequalities which will be used in this article.Then in the third chapter,we give conclusions and lemmas which is the center of this paper,and of course we give the detailed proof process.Lastly,We summarize the work we have done and point out the future of the research direction according to the conclusions.