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

Gess B, Hofmanová M (2018)
ANNALS OF PROBABILITY 46(5): 2495-2544.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Abstract / Bemerkung
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].
Stichworte
Quasilinear degenerate parabolic stochastic partial differential; equation; kinetic formulation; kinetic solution; velocity averaging; lemmas; renormalized solutions
Erscheinungsjahr
2018
Zeitschriftentitel
ANNALS OF PROBABILITY
Band
46
Ausgabe
5
Seite(n)
2495-2544
ISSN
0091-1798
Page URI
https://pub.uni-bielefeld.de/record/2931096

Zitieren

Gess B, Hofmanová M. Well-posedness and regularity for quasilinear degenerate parabolic-hyperbolic SPDE. ANNALS OF PROBABILITY. 2018;46(5):2495-2544.
Gess, B., & Hofmanová, M. (2018). Well-posedness and regularity for quasilinear degenerate parabolic-hyperbolic SPDE. ANNALS OF PROBABILITY, 46(5), 2495-2544. doi:10.1214/17-AOP1231
Gess, B., and Hofmanová, M. (2018). Well-posedness and regularity for quasilinear degenerate parabolic-hyperbolic SPDE. ANNALS OF PROBABILITY 46, 2495-2544.
Gess, B., & Hofmanová, M., 2018. Well-posedness and regularity for quasilinear degenerate parabolic-hyperbolic SPDE. ANNALS OF PROBABILITY, 46(5), p 2495-2544.
B. Gess and M. Hofmanová, “Well-posedness and regularity for quasilinear degenerate parabolic-hyperbolic SPDE”, ANNALS OF PROBABILITY, vol. 46, 2018, pp. 2495-2544.
Gess, B., Hofmanová, M.: Well-posedness and regularity for quasilinear degenerate parabolic-hyperbolic SPDE. ANNALS OF PROBABILITY. 46, 2495-2544 (2018).
Gess, Benjamin, and Hofmanová, Martina. “Well-posedness and regularity for quasilinear degenerate parabolic-hyperbolic SPDE”. ANNALS OF PROBABILITY 46.5 (2018): 2495-2544.
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