Stochastic Entropy Solutions for Stochastic Scalar Balance Laws
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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.
1994 ◽
Vol 14
(3)
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pp. 261-271
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2018 ◽
Vol 5
(1)
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pp. 102-112
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2020 ◽
Vol 268
(9)
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pp. 5469-5490
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