Well-posedness and regularity for quasilinear degenerate parabolic-hyperbolic SPDE
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Publication:1800811
DOI10.1214/17-AOP1231zbMATH Open1428.60090arXiv1611.03600MaRDI QIDQ1800811
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Publication date: 24 October 2018
Published in: (Search for Journal in Brave)
Abstract: 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 setting requiring no growth assumptions on the nonlinearities. In addition, we prove a comparison result and an -contraction property for the solutions.
Full work available at URL: https://arxiv.org/abs/1611.03600
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