QUASILINEAR ROUGH EVOLUTION EQUATIONS

• 成果类型: Article
• 署名作者: Hocquet, Antoine; Neamtu, Alexandra
• 署名单位: Technical University of Berlin; University of Konstanz
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/24-AAP2065
• 发表日期: 2024
• 页码: 4268-4309
• 关键词: partial-differential-equations; random dynamical-systems; mild solutions; EXISTENCE

摘要

We investigate the abstract Cauchy problem for a quasilinear parabolic equation in a Banach space of the form dut - Lt(ut)ut dt = Nt(ut)dt + F(ut) d X t , where X is a gamma-H & ouml;lder rough path for gamma E ( 1 / 3 , 1/2). We explore the mild formulation that combines functional analysis techniques and controlled rough paths theory which entail the local well-posedness of such equations. We apply our results to the stochastic Landau-Lifshitz-Gilbert and Shigesada-Kawasaki-Teramoto equation.