Stochastic Entropy Solutions for Stochastic Nonlinear Transport Equations

This paper considers the existence and uniqueness of stochastic entropy solution for a nonlinear transport equation with a stochastic perturbation. The uniqueness is based on the doubling variable method. For the existence, we develop a new scheme of parabolic approximation motivated by the method o...

Descripción completa

Detalles Bibliográficos
Autores principales: Tian, Rongrong, Tang, Yanbin
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2018
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7512913/
https://www.ncbi.nlm.nih.gov/pubmed/33265486
http://dx.doi.org/10.3390/e20060395
_version_ 1783586266983432192
author Tian, Rongrong
Tang, Yanbin
author_facet Tian, Rongrong
Tang, Yanbin
author_sort Tian, Rongrong
collection PubMed
description This paper considers the existence and uniqueness of stochastic entropy solution for a nonlinear transport equation with a stochastic perturbation. The uniqueness is based on the doubling variable method. For the existence, we develop a new scheme of parabolic approximation motivated by the method of vanishing viscosity given by Feng and Nualart (J. Funct. Anal. 2008, 255, 313–373). Furthermore, we prove the continuous dependence of stochastic strong entropy solutions on the coefficient b and the nonlinear function f.
format Online
Article
Text
id pubmed-7512913
institution National Center for Biotechnology Information
language English
publishDate 2018
publisher MDPI
record_format MEDLINE/PubMed
spelling pubmed-75129132020-11-09 Stochastic Entropy Solutions for Stochastic Nonlinear Transport Equations Tian, Rongrong Tang, Yanbin Entropy (Basel) Article This paper considers the existence and uniqueness of stochastic entropy solution for a nonlinear transport equation with a stochastic perturbation. The uniqueness is based on the doubling variable method. For the existence, we develop a new scheme of parabolic approximation motivated by the method of vanishing viscosity given by Feng and Nualart (J. Funct. Anal. 2008, 255, 313–373). Furthermore, we prove the continuous dependence of stochastic strong entropy solutions on the coefficient b and the nonlinear function f. MDPI 2018-05-23 /pmc/articles/PMC7512913/ /pubmed/33265486 http://dx.doi.org/10.3390/e20060395 Text en © 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Tian, Rongrong
Tang, Yanbin
Stochastic Entropy Solutions for Stochastic Nonlinear Transport Equations
title Stochastic Entropy Solutions for Stochastic Nonlinear Transport Equations
title_full Stochastic Entropy Solutions for Stochastic Nonlinear Transport Equations
title_fullStr Stochastic Entropy Solutions for Stochastic Nonlinear Transport Equations
title_full_unstemmed Stochastic Entropy Solutions for Stochastic Nonlinear Transport Equations
title_short Stochastic Entropy Solutions for Stochastic Nonlinear Transport Equations
title_sort stochastic entropy solutions for stochastic nonlinear transport equations
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7512913/
https://www.ncbi.nlm.nih.gov/pubmed/33265486
http://dx.doi.org/10.3390/e20060395
work_keys_str_mv AT tianrongrong stochasticentropysolutionsforstochasticnonlineartransportequations
AT tangyanbin stochasticentropysolutionsforstochasticnonlineartransportequations

Ejemplares similares