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. 
Benjamin Gess, Martina Hofmanov\'a
math.PR math.AP