Stability of hyperbolic-parabolic mixed type equations with partial boundary condition

被引：18

作者：

Zhan, Huashui ^{[1
]}

Feng, Zhaosheng ^{[2
]}

机构：

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

[2] Univ Texas Rio Grande Valley, Sch Math & Stat Sci, Edinburg, TX 78539 USA

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2018年 / 264卷 / 12期

关键词：

Hyperbolic-parabolic equation; Stability; Partial boundary condition; Well-posedness; Entropy solution; DIRICHLET PROBLEMS; ENTROPY SOLUTIONS; UNIQUENESS;

D O I：

10.1016/j.jde.2018.02.019

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we are concerned with the hyperbolic-parabolic mixed type equations with the non-homogeneous boundary condition. If it is degenerate on the boundary, the part of the boundary whose boundary value should be imposed, is determined by the entropy condition from the convection term. If there is no convection term in the equation, we show that the stability of solutions can be proved without any boundary condition. If the equation is completely degenerate, we show that the stability of solutions can be established just based on the partial boundary condition. (C) 2018 Elsevier Inc. All rights reserved.

引用

页码：7384 / 7411

页数：28

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