ANALYSIS OF A DIFFUSE INTERFACE APPROACH TO AN ADVECTION DIFFUSION EQUATION ON A MOVING SURFACE

被引：23

作者：

Elliott, Charles M. ^{[1
]}

Stinner, Bjoern

机构：

[1] Univ Warwick, Math Inst, Coventry CV4 7AL, W Midlands, England

来源：

MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES | 2009年 / 19卷 / 05期

关键词：

Moving surface; surface partial differential equation; weighted Sobolev space; asymptotic analysis; PARTIAL-DIFFERENTIAL-EQUATIONS; FINITE-ELEMENT-METHOD; PARABOLIC EQUATIONS; GENERAL GEOMETRIES; IMPLICIT SURFACES; THIN DOMAINS; PDES;

D O I：

10.1142/S0218202509003620

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：787 / 802

页数：16

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