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On a phase field problem driven by interface area and interface curvature

Published online by Cambridge University Press:  05 November 2009

XIAOFENG REN  and
JUNCHENG WEI
XIAOFENG REN
Affiliation:
Department of Mathematics and Statistics, The George Washington University, Washington, DC 20052, USA email: ren@gwu.edu
JUNCHENG WEI
Affiliation:
Department of Mathematics, Chinese University of Hong Kong, Hong Kong, P.R. China
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Abstract

A two component system driven by both interface area and interface curvature is studied with a new phase field model. We show that if the curvature impact in the system is strong enough, there exist bubble profiles. A bubble profile describes a pattern of an inner core of one component surround by an outer membrane of the other component. It is a radial solution to a fourth-order nonlinear partial differential equation. We show the existence of such profiles in all dimensions, although the profile is unstable if the dimension is greater than 2.

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Type
Papers
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European Journal of Applied Mathematics , Volume 20 , Issue 6 , December 2009 , pp. 531 - 556
Copyright
Copyright © Cambridge University Press 2009

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