TY  - JOUR
AB  - 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].
DA  - 2018
DO  - 10.1214/17-AOP1231
KW  - Quasilinear degenerate parabolic stochastic partial differential
KW  - equation
KW  - kinetic formulation
KW  - kinetic solution
KW  - velocity averaging
KW  - lemmas
KW  - renormalized solutions
LA  - eng
IS  - 5
M2  - 2495
PY  - 2018
SN  - 0091-1798
SP  - 2495-2544
T2  - ANNALS OF PROBABILITY
TI  - Well-posedness and regularity for quasilinear degenerate parabolic-hyperbolic SPDE
UR  - https://nbn-resolving.org/urn:nbn:de:0070-pub-29310961
Y2  - 2024-11-21T22:17:16
ER  -