Well-posedness for stochastic scalar conservation laws with the initial-boundary condition

被引：3
|
作者：
Kobayasi, Kazuo [1 ]
Noboriguchi, Dai [2 ]
机构：
[1] Waseda Univ, Dept Math Educ & Integrated Arts & Sci, Shinjuku Ku, 1-6-1 Nishi Waseda, Tokyo 1698050, Japan
[2] Kushiro Coll, Natl Inst Technol, Gen Educ, Dept Creat Engn, 2-32-1 Otanoshike Nishi, Kushiro, Hokkaido 0840916, Japan
来源：
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2018年 / 461卷 / 02期
关键词：
Stochastic partial differential equations; Conservation laws; Kinetic formulation; Initial-boundary value problem; PARTIAL-DIFFERENTIAL-EQUATIONS; FORMULATION;
D O I：
10.1016/j.jmaa.2018.01.054
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we are interested in the initial-(non-homogeneous) Dirichlet boundary value problem for a multi-dimensional scalar non-linear conservation law with a multiplicative stochastic forcing. We introduce a notion of "renormalized" kinetic formulations in which the kinetic defect measures on the boundary of a domain are truncated. In such a kinetic formulation we establish a result of well-posedness of the initial-boundary value problem under only the assumptions (H-1), (H-2) and (H-3) stated below, which are very similar ones in [6]. (C) 2018 Elsevier Inc. All rights reserved.
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页码：1416 / 1458
页数：43
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