一类半线性分数阶反应扩散方程解的整体存在性

Global Existence of Solutions to Semilinear Fractional Reaction-Diffusion Equation

研究了齐次Dirichlet边界下一类半线性分数阶反应扩散方程解的整体存在性和渐近行为.通过Caffarelli-Silvestre延拓方法将非局部的分数阶Laplacian算子转化为局部可变分的算子,再用Galёrkin方法在适当的假设条件下得到方程整体解的存在性,最后利用一些基本不等式得到方程解的渐近行为.

In this paper,the global solution and long time asymptotic behavior of the semilinear fractional reaction-diffusion equation have been studied with homogeneous Dirichlet boundary.The Caffarelli-Silvestre extension method was used to transform the nonlocal Laplacian problem into a variable local problem.Combing Galёrkin method,we can get the existence of solution.Lastly we utilize some inequalities to get long time asymptotic behavior of global solutions.