Journal
JOURNAL OF FUNCTIONAL ANALYSIS
Volume 259, Issue 4, Pages 1014-1042Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jfa.2010.02.016
Keywords
Stochastic partial differential equations; Conservation laws; Kinetic formulation; Entropy solutions
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We show that the Cauchy Problem for a randomly forced, periodic multi-dimensional scalar first-order conservation law with additive or multiplicative noise is well posed: it admits a unique solution, characterized by a kinetic formulation of the problem, which is the limit of the solution of the stochastic parabolic approximation. (C) 2010 Elsevier Inc. All rights reserved.
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