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Open AccessArticle

Stochastic Entropy Solutions for Stochastic Nonlinear Transport Equations

School of Mathematics and Statistics, Hubei Key Laboratory of Engineering Modeling and Scientific Computing, Huazhong University of Science and Technology, Wuhan 430074, China
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Entropy 2018, 20(6), 395; https://doi.org/10.3390/e20060395
Received: 26 April 2018 / Revised: 15 May 2018 / Accepted: 21 May 2018 / Published: 23 May 2018
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. View Full-Text
Keywords: nonlinear transport equation; stochastic (strong) entropy solution; uniqueness; existence nonlinear transport equation; stochastic (strong) entropy solution; uniqueness; existence
MDPI and ACS Style

Tian, R.; Tang, Y. Stochastic Entropy Solutions for Stochastic Nonlinear Transport Equations. Entropy 2018, 20, 395.

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