THE STABILITY OF WEAK SOLUTIONS TO AN ANISOTROPIC POLYTROPIC INFILTRATION EQUATION

被引：0

作者：

Zhan, Huashui ^{[1
]}

机构：

[1] Xiamen Univ Technol, Sch Appl Math, Xiamen 361024, Fujian, Peoples R China

来源：

JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY | 2021年 / 58卷 / 05期

关键词：

The anisotropic polytropic infiltration equation; the weak characteristic function method; stability; boundary value condition; DEGENERATE PARABOLIC EQUATIONS; CAUCHY-PROBLEM; LOCALIZATION PROPERTIES; UNIQUENESS; EXISTENCE; SYSTEMS;

D O I：

10.4134/JKMS.j200369

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper considers an anisotropic polytropic infiltration equation with a source term u(t) = Sigma(N)(i=1) partial derivative/partial derivative x(i) (a(i)(x)vertical bar u vertical bar(alpha i)vertical bar u(xi)vertical bar p(i)(-2)u(xi)) + f(x, t, u), where p(i) > 1, alpha(i) > 0, a(i)(x) >= 0. The existence of weak solution is proved by parabolically regularized method. Based on local integrability u(xi) is an element of W-loc(1, pi )(Omega), the stability of weak solutions is proved without boundary value condition by the weak characteristic function method. One of the essential characteristics of an anisotropic equation different from an isotropic equation is found originally.

引用

页码：1109 / 1129

页数：21

共 36 条

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