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arXiv · 1611.03600

Well-posedness and regularity for quasilinear degenerate parabolic-hyperbolic SPDE

Benjamin Gess·Martina Hofmanová
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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 $L^1$ setting requiring no growth assumptions on the nonlinearities. In addition, we prove a comparison result and an $L^1$-contraction property for the solutions.

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Benjamin Gess, Martina Hofmanová. 2016-11-11. Well-posedness and regularity for quasilinear degenerate parabolic-hyperbolic SPDE. https://arxiv.org/abs/1611.03600

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