Year: 2023
Type: article
Abstract: We prove a short time existence result for a system consisting of a geometric evolution equation for a hypersurface and a parabolic equation on this evolving hypersurface. More precisely, we discuss a mean curvature flow scaled with a term that depends on a quantity defined on the surface coupled to a diffusion equation for that quantity. The proof is based on a splitting ansatz, solving both equations separately using linearization and a contraction argument. Our result is formulated for the case of immersed hypersurfaces and yields a uniform lower bound on the existence time that allows for small changes in the initial value of the height function.
Source: Journal of Evolution Equations
Authors: Helmut Abels, Felicitas Bürger, Harald Garcke
Institution: University of Regensburg
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,890
Funder: Deutsche Forschungsgemeinschaft
Award: G5450455261
OpenAlex ID: W4313816490