The Nonlocal Porous Medium Equation: Barenblatt Profiles and Other Weak Solutions

被引：58
|
作者：
Biler, Piotr [1 ]
Imbert, Cyril [2 ]
Karch, Grzegorz [1 ]
机构：
[1] Uniwersytet Wroclawski, Inst Matemat, PL-50384 Wroclaw, Poland
[2] Univ Paris Est Creteil, CNRS, UMR 8050, F-94010 Creteil, France
来源：
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS | 2015年 / 215卷 / 02期
关键词：
PRINCIPLE;
D O I：
10.1007/s00205-014-0786-1
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A degenerate nonlinear nonlocal evolution equation is considered; it can be understood as a porous medium equation whose pressure law is nonlinear and nonlocal. We show the existence of sign-changing weak solutions to the corresponding Cauchy problem. Moreover, we construct explicit compactly supported self-similar solutions which generalize Barenblatt profiles-the well-known solutions of the classical porous medium equation.
引用
收藏
页码：497 / 529
页数：33
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