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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: [email protected]
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.

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

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