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.

引用

页码：1416 / 1458

页数：43

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