Quasilinear rough evolution equations
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.
Authors
- Antoine Hocquet (ORCID: https://orcid.org/0000-0002-3017-5421)
- Alexandra Neamţu (ORCID: https://orcid.org/0000-0002-0782-2133)
Institutions
- University of Konstanz (DE)
- Institute of Mathematics and Informatics (BG)
- Czech Academy of Sciences, Institute of Mathematics (CZ)
- Technische Universität Berlin (DE)
Publication Details
- Journal
- The Annals of Applied Probability
- Published
- 2024-09-27
- DOI
- https://doi.org/10.1214/24-aap2065
- Citations
- 4
- Primary Topic
- Advanced Numerical Methods in Computational Mathematics
- Type
- article
- Field-Weighted Citation Impact
- 1.50