{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:51:57Z","timestamp":1760241117563,"version":"build-2065373602"},"reference-count":38,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2019,11,22]],"date-time":"2019-11-22T00:00:00Z","timestamp":1574380800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>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.<\/jats:p>","DOI":"10.3390\/e21121142","type":"journal-article","created":{"date-parts":[[2019,11,22]],"date-time":"2019-11-22T09:02:52Z","timestamp":1574413372000},"page":"1142","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Stochastic Entropy Solutions for Stochastic Scalar Balance Laws"],"prefix":"10.3390","volume":"21","author":[{"given":"Jinlong","family":"Wei","sequence":"first","affiliation":[{"name":"School of Statistics and Mathematics, Zhongnan University of Economics and Law, Wuhan 430073, China"}]},{"given":"Bin","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China"}]},{"given":"Rongrong","family":"Tian","sequence":"additional","affiliation":[{"name":"College of Science, Wuhan University of Technology, Wuhan 430070, China"}]},{"given":"Liang","family":"Ding","sequence":"additional","affiliation":[{"name":"School of Data Science and Information Engineering, Guizhou Minzu University, Guiyang 550025, China"}]}],"member":"1968","published-online":{"date-parts":[[2019,11,22]]},"reference":[{"key":"ref_1","first-page":"228","article-title":"First-order quasilinear equations in several independent variables","volume":"81","year":"1970","journal-title":"Math. 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