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Stochastic Entropy Solutions for Stochastic Scalar Balance Laws

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School of Statistics and Mathematics, Zhongnan University of Economics and Law, Wuhan 430073, China
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School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China
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College of Science, Wuhan University of Technology, Wuhan 430070, China
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School of Data Science and Information Engineering, Guizhou Minzu University, Guiyang 550025, China
*
Author to whom correspondence should be addressed.
Entropy 2019, 21(12), 1142; https://doi.org/10.3390/e21121142
Received: 31 October 2019 / Revised: 20 November 2019 / Accepted: 21 November 2019 / Published: 22 November 2019
We are concerned with the initial value problem for a multidimensional balance law with multiplicative stochastic perturbations of Brownian type. Using the stochastic kinetic formulation and the Bhatnagar-Gross-Krook approximation, we prove the uniqueness and existence of stochastic entropy solutions. Furthermore, as applications, we derive the uniqueness and existence of the stochastic entropy solution for stochastic Buckley-Leverett equations and generalized stochastic Burgers type equations.
Keywords: Uniqueness; Existence; Stochastic entropy solution; Stochastic kinetic formulation; Bhatnagar-Gross-Krook approximation Uniqueness; Existence; Stochastic entropy solution; Stochastic kinetic formulation; Bhatnagar-Gross-Krook approximation
MDPI and ACS Style

Wei, J.; Liu, B.; Tian, R.; Ding, L. Stochastic Entropy Solutions for Stochastic Scalar Balance Laws. Entropy 2019, 21, 1142.

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