具有幂函数反应项的分数阶多孔介质方程解的爆破性  

Blow-up of Solution to a Fractional Porous Medium Equation with a Power Function Reaction Term

作　　者：李建军[1] 王看看 高晓茹 刘文涛 LI Jianjun;WANG Kankan;GAO Xiaoru;LIU Wentao(School of Sciences,Liaoning Technical University,Fuxin,Liaoning,123000,P.R.China)

机构地区：[1]辽宁工程技术大学理学院,辽宁阜新123000

出　　处：《数学进展》2024年第2期349-358,共10页Advances in Mathematics（China）

基　　金：辽宁工程技术大学学科创新团队资助项目(No.LNTU20TD-13)。

摘　　要：本文研究了一类具有幂函数反应项的分数阶多孔介质方程Dirichlet边值问题解的爆破性.首先,由于分数阶Laplace算子的非局部性,利用Caffareli-Silvestre扩展方法将非局部的原问题等价地转化为具有动力边界条件的局部椭圆型方程定解问题.然后,在此基础上,通过凹函数法得到局部解的爆破性;最后,利用全局解的一致有界性,得到方程全局解的长时间渐近性态.The blow-up of a Dirichlet boundary value problem for a class of fractional porous medium equations with a power function reaction term was studied.First,due to the non-locality of fractional Laplacian operator,the non-local problem is converted into a local elliptic equation with dynamic boundary conditions by using Caffarelli–Silvestre extension method.Second,being based upon this,the blow-up of local solution was obtained by concave function method.Finally,the long time asymptotic behaviors of the global solution of the equation were obtained by using the uniform boundedness of the global solution.

关 键 词：幂函数反应项 爆破 长时间渐近性态 动力边界条件 分数阶多孔介质方程 

分 类 号：O175.2[理学—数学]