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

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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.