Translator Disclaimer
September 2018 Well-posedness and regularity for quasilinear degenerate parabolic-hyperbolic SPDE
Benjamin Gess, Martina Hofmanová
Ann. Probab. 46(5): 2495-2544 (September 2018). 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, generalizing the results obtained in [Ann. Probab. 44 (2016) 1916–1955].

Citation

Download Citation

Benjamin Gess. Martina Hofmanová. "Well-posedness and regularity for quasilinear degenerate parabolic-hyperbolic SPDE." Ann. Probab. 46 (5) 2495 - 2544, September 2018. https://doi.org/10.1214/17-AOP1231

Information

Received: 1 June 2017; Published: September 2018
First available in Project Euclid: 24 August 2018

zbMATH: 06964342
MathSciNet: MR3846832
Digital Object Identifier: 10.1214/17-AOP1231

Subjects:
Primary: 35R60, 60H15

Rights: Copyright © 2018 Institute of Mathematical Statistics

JOURNAL ARTICLE
50 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.46 • No. 5 • September 2018
Back to Top