Year: 2024
Type: article
Abstract: We investigate the abstract Cauchy problem for a quasilinear parabolic equation in a Banach space of the form dut−Lt(ut)utdt=Nt(ut)dt+F(ut)·dXt, where X is a γ-Hölder rough path for γ∈(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.
DOI: 10.1214/24-aap2065
Authors: Antoine Hocquet, Alexandra Neamţu
Institutions: Technische Universität Berlin, University of Konstanz
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Deutsche Forschungsgemeinschaft
Award: G6729069662
OpenAlex ID: W4402933467