Heterogeneous stochastic scalar conservation laws with non-homogeneous Dirichlet boundary conditions-Reference-Cited by-同舟云学术

Heterogeneous stochastic scalar conservation laws with non-homogeneous Dirichlet boundary conditions

Published:2018-06 Issue:02 Volume:15 Page:291-328
ISSN:0219-8916
Container-title:Journal of Hyperbolic Differential Equations
language:en
Short-container-title:J. Hyper. Differential Equations

Author:

Lv Guangying¹²,Wu Jiang-Lun³⁴

Affiliation:

1. School of Mathematical Science, Nanjing Normal University, Nanjing 210023, P. R. China

2. Institute of Applied Mathematics, Henan University, Kaifeng 475004, P. R. China

3. School of Mathematics, Northwest University, Xi’an, Shaanxi Province 710127, P. R. China

4. Department of Mathematics, College of Science, Swansea University, Singleton Park, Swansea SA2 8PP, UK

Abstract

We introduce a notion of stochastic entropy solutions for heterogeneous scalar conservation laws with multiplicative noise on a bounded domain with non-homogeneous boundary condition. Using the concept of measure-valued solutions and Kruzhkov’s semi-entropy formulations, we show the existence and uniqueness of stochastic entropy solutions. Moreover, we establish an explicit estimate for the continuous dependence of stochastic entropy solutions on the flux function and the random source function.

Publisher

World Scientific Pub Co Pte Lt

Subject

General Mathematics,Analysis

Link

https://www.worldscientific.com/doi/pdf/10.1142/S021989161850011X

Reference33 articles.

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