Partial boundary value condition for a nonlinear degenerate parabolic equation

被引：15
|
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 | 2019年 / 267卷 / 05期
关键词：
Degenerate parabolic equation; Boundary value condition; Stability; Hausdorff measure; ENTROPY SOLUTIONS; WELL-POSEDNESS; CAUCHY-PROBLEM; UNIQUENESS; STABILITY;
D O I：
10.1016/j.jde.2019.03.032
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, a nonlinear degenerate parabolic equation is considered. By proposing a new partial boundary value condition and constructing special test functions, we prove the stability of the solutions by means of the Kruzkov bi-variables method. Moreover, we show that if there is an interaction between the diffusion term and the convection term, the stability can be established without any boundary value condition. (C) 2019 Elsevier Inc. All rights reserved.
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页码：2874 / 2890
页数：17
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