WELL-POSEDNESS AND REGULARITY FOR QUASILINEAR DEGENERATE PARABOLIC-HYPERBOLIC SPDE

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 existenc...

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Bibliographic Details
Published in:The Annals of probability 2018-09, Vol.46 (5), p.2495-2544
Main Authors: Gess, Benjamin, Hofmanová, Martina
Format: Article
Language:English
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Summary: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 L¹ setting requiring no growth assumptions on the nonlinearities. In addition, we prove a comparison result and an L¹-contraction property for the solutions, generalizing the results obtained in [Ann. Probab. 44 (2016) 1916–1955].
ISSN:0091-1798
2168-894X
DOI:10.1214/17-AOP1231