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2017 An $L^1$-theory for scalar conservation laws with multiplicative noise on a periodic domain
Dai Noboriguchi
Nihonkai Math. J. 28(1): 43-53 (2017).

Abstract

We study the Cauchy problem for a multi-dimensional scalar conservation law with a multiplicative noise. Our aim is to give the well-posedness of an $L^1$-solution characterized by a kinetic formulation under appropriate assumptions. In particular, we focus on the existence of such a solution.

Funding Statement

The author has been supported by Waseda University Grant for Special Research Projects (No. 2015S-042).

Citation

Download Citation

Dai Noboriguchi. "An $L^1$-theory for scalar conservation laws with multiplicative noise on a periodic domain." Nihonkai Math. J. 28 (1) 43 - 53, 2017.

Information

Received: 29 December 2015; Revised: 2 July 2016; Published: 2017
First available in Project Euclid: 7 March 2018

zbMATH: 06881241
MathSciNet: MR3771367

Subjects:
Primary: 35L04
Secondary: 60H15

Rights: Copyright © 2017 Niigata University, Department of Mathematics

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Vol.28 • No. 1 • 2017
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