含变源的多孔介质方程的解的爆破  

Blow⁃up to a Porous Medium Equation Involving Variable Source

作　　者：郭晋容 唐亚勇[1] GUO Jinrong;TANG Yayong(College of Mathematics,Sichuan University,Chengdu,Sichuan,610064,China)

机构地区：[1]四川大学数学学院,四川成都610064

出　　处：《宜宾学院学报》2022年第6期79-84,共6页Journal of Yibin University

基　　金：国家自然科学基金项目(11201380);四川省应用基础研究基金项目(2018JY0334)。

摘　　要：为了研究含变源的多孔介质方程的数学模型的解的爆破现象,对一类含变源的多孔介质方程在初始能量为非正和初始能量为正这两种情形进行研究,得到了在初始能量为非正时模型的解会在有限时间内爆破的结论,建立了在初始能量为正时解的爆破条件,并用反证法对爆破解的爆破时间的上界进行了估计.In order to study a phenomenon that is called blow-up in a porous medium equation involving variable source,a po⁃rous medium equation involving variable source are studied with non-positive initial energy and positive initial energy.It is con⁃cluded that the solution of the model will blow up in finite time when the initial energy is non-positive,the blow-up condition of the solution with positive initial energy is established,and the upper bound of the blow-up time for the blow-up solutions is estimated by using reduction to absurdity.

关 键 词：多孔介质方程 正初始能量 爆破 爆破时间 

分 类 号：O19[理学—数学] O29[理学—基础数学]