WELL-POSEDNESS AND REGULARITY FOR QUASILINEAR DEGENERATE PARABOLIC-HYPERBOLIC SPDE

• 成果类型: Article
• 署名作者: Gess, Benjamin; Hofmanova, Martina
• 署名单位: Max Planck Society; University of Bielefeld; Technical University of Berlin
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/17-AOP1231
• 发表日期: 2018
• 页码: 2495-2544
• 关键词: scalar conservation-laws; generalized porous-media; gross-krook approximation; cauchy-problem; renormalized solutions; kinetic formulations; EXISTENCE; uniqueness; EQUATIONS; ergodicity

摘要

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].