Quasilinear parabolic stochastic partial differential equations: Existence, uniqueness

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:127

Article

Hofmanova, Martina¹  Zhang, Tusheng² 

[1] Tech Univ Berlin, Inst Math, Str 17 Juni 136, D-10623 Berlin, Germany

[2] Univ Manchester, Sch Math, Oxford Rd, Manchester M13 9PL, Lancs, England

关键词: Quasilinear stochastic partial differential equations;    Strong solutions;    Energy inequality;   

DOI  :  10.1016/j.spa.2017.01.010

来源: Elsevier

【 摘 要 】

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 Ito's formula for the L-1-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. Crown Copyright (C) 2017 Published by Elsevier B.V. All rights reserved.

【 授权许可】

Free