Short time existence for coupling of scaled mean curvature flow and diffusion

URN to cite this document:: urn:nbn:de:bvb:355-epub-535057
DOI to cite this document:: 10.5283/epub.53505

Abels, Helmut

; Bürger, Felicitas ; Garcke, Harald

License: Creative Commons Attribution 4.0
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Date of publication of this fulltext: 10 Jan 2023 08:34

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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 ...