Quasilinear parabolic stochastic partial differential equations: Existence, uniqueness

Martina Hofmanová and Tusheng Zhang

Stochastic Processes and their Applications, 2017, vol. 127, issue 10, 3354-3371

Abstract: We present a direct approach to existence and uniqueness of strong (in the probabilistic sense) and weak (in the PDE sense) solutions to quasilinear stochastic partial differential equations, which are neither monotone nor locally monotone. The proof of uniqueness is very elementary, based on a new method of applying Itô’s formula for the L1-norm. The proof of existence relies on a recent regularity result and is direct in the sense that it does not rely on the stochastic compactness method.

Keywords: Quasilinear stochastic partial differential equations; Strong solutions; Energy inequality (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.spa.2017.01.010

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