Elliott, Charles M. and Stinner, Björn (2009) Analysis of a diffuse interface approach to an advection diffusion equation on a moving surface. Mathematical Models and Methods in Applied Sciences, Vol.19 (No.5). pp. 787-802. doi:10.1142/S0218202509003620 ISSN 0218-2025.

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Abstract

A diffuse interface model for an advection diffusion equation on a moving surface is formulated involving a small parameter epsilon related to the thickness of the interfacial layer. The coefficient functions degenerate on the boundary of the diffuse interface. In appropriately weighted Sobolev spaces, existence and uniqueness of weak solutions is shown. Using energy methods the convergence of solutions to the diffuse interface model to the solution to the equation on the moving surface as epsilon -> 0 is proved. The approach is intended to be applied to phase field models describing the surface motion. Among other problems we have surfactants on liquid-liquid interfaces and species diffusion on moving grain boundaries in mind.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science, Engineering and Medicine > Science > Mathematics
Journal or Publication Title:	Mathematical Models and Methods in Applied Sciences
Publisher:	World Scientific Publishing Co. Pte. Ltd.
ISSN:	0218-2025
Official Date:	May 2009
Dates:	Date Event May 2009 Published
Volume:	Vol.19
Number:	No.5
Number of Pages:	16
Page Range:	pp. 787-802
DOI:	10.1142/S0218202509003620
Status:	Peer Reviewed
Publication Status:	Published
Funder:	German Research Foundation (DFG)
Grant number:	Sti 579/1-1,2

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