Existence of weak solutions for porous medium equation with a divergence type of drift term in a bounded domain

被引：1
作者：
Hwang, Sukjung [1 ]
Kang, Kyungkeun [2 ]
Kim, Hwa Kil [3 ]
机构：
[1] Chungbuk Natl Univ, Dept Math Educ, Cheongju 28644, South Korea
[2] Yonsei Univ, Dept Math, Seoul 03722, South Korea
[3] Hannam Univ, Dept Math Educ, Daejeon 34430, South Korea
来源：
JOURNAL OF DIFFERENTIAL EQUATIONS | 2024年 / 389卷
关键词：
Porous medium equation; Weak solution; Wasserstein space; A bounded domain; GLOBAL EXISTENCE; REGULARITY; MODEL;
D O I：
10.1016/j.jde.2024.01.028
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We study porous medium equations with a divergence form of drift terms in a bounded domain with no-flux lateral boundary conditions. We establish Lq-weak solutions for 1 <= q < infinity in Wasserstein space under appropriate conditions on the drift, which is an extension of authors' previous works done in the whole space into the case of bounded domains. Applying existence results to a certain Keller-Segel equation of consumption type, construction of L-q -weak solutions is also made, in case that the equation of a biological organism is of porous medium type. (c) 2024 Elsevier Inc. All rights reserved.
引用
收藏
页码：361 / 414
页数：54
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