BOUNDED WEAK SOLUTIONS TO THE THIN FILM MUSKAT PROBLEM VIA AN INFINITE FAMILY OF LIAPUNOV FUNCTIONALS

被引：3

作者：

Laurencot, Philippe ^{[1
]}

Matioc, Bogdan-Vasile ^{[2
]}

机构：

[1] Univ Toulouse, Inst Math Toulouse, UMR 5219, CNRS, F-31062 Toulouse 9, France

[2] Univ Regensburg, Fak Math, D-93040 Regensburg, Germany

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2022年 / 375卷 / 08期

关键词：

FLOWS;

D O I：

10.1090/tran/8688

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A countably infinite family of Liapunov functionals is constructed for the thin film Muskat problem, which is a second-order degenerate parabolic system featuring cross-diffusion. More precisely, for each n >= 2 we construct an homogeneous polynomial of degree n, which is convex on [0, infinity)2, with the property that its integral is a Liapunov functional for the problem. Existence of global bounded non-negative weak solutions is then shown in one space dimension.

引用

页码：5963 / 5986

页数：24

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