Well-posedness and regularity for quasilinear degenerate parabolic-hyperbolic SPDE
- Authors: Benjamin Gess, Martina Hofmanová
- Preprint year: 2016
- First public date: 2016-11-11
- arXiv: 1611.03600
- Status: Published
- Publication type: Journal article
- Publication year: 2018
- Journal: The annals of probability, 46 (2018) 5, pp. 2495-2544
- DOI: 10.1214/17-AOP1231
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.