## Nihonkai Mathematical Journal

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

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

#### 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