Nihonkai Mathematical Journal

An $L^1$-theory for scalar conservation laws with multiplicative noise on a periodic domain

Dai Noboriguchi

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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.

Note

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

Article information

Source
Nihonkai Math. J., Volume 28, Number 1 (2017), 43-53.

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

Permanent link to this document
https://projecteuclid.org/euclid.nihmj/1520391680

Mathematical Reviews number (MathSciNet)
MR3771367

Zentralblatt MATH identifier
06881241

Subjects
Primary: 35L04: Initial-boundary value problems for first-order hyperbolic equations
Secondary: 60H15: Stochastic partial differential equations [See also 35R60]

Keywords
stochastic partial differential equations conservation laws kinetic formulation initial value problem

Citation

Noboriguchi, Dai. An $L^1$-theory for scalar conservation laws with multiplicative noise on a periodic domain. Nihonkai Math. J. 28 (2017), no. 1, 43--53. https://projecteuclid.org/euclid.nihmj/1520391680


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