期刊
ANNALS OF PROBABILITY
卷 46, 期 5, 页码 2495-2544出版社
INST MATHEMATICAL STATISTICS-IMS
DOI: 10.1214/17-AOP1231
关键词
Quasilinear degenerate parabolic stochastic partial differential equation; kinetic formulation; kinetic solution; velocity averaging lemmas; renormalized solutions
We study quasilinear degenerate parabolic-hyperbolic stochastic partial differential equations with general multiplicative noise within the framework of kinetic solutions. Our results are twofold: First, we establish new regularity results based on averaging techniques. Second, we prove the existence and uniqueness of solutions in a full L-1 setting requiring no growth assumptions on the nonlinearities. In addition, we prove a comparison result and an L-1 -contraction property for the solutions, generalizing the results obtained in [Ann. Probab. 44 (2016) 1916-1955].
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