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 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].