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Motion of bubbles towards the boundary for the Cahn–Hilliard equation

Published online by Cambridge University Press:  14 April 2004

N. D. ALIKAKOS ,
G. FUSCO  and
G. KARALI
N. D. ALIKAKOS
Affiliation:
Department of Mathematics, University of Athens, Athens, Greece
G. FUSCO
Affiliation:
Dipartimento di Mathematica, Universita di L'Aquila, Italy
G. KARALI
Affiliation:
Department of Mathematics, University of Athens, Athens, Greece
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Abstract

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In this work we describe some aspects of the dynamics of the Cahn–Hilliard equation. In particular, we consider the dynamics of ‘bubble’ solutions that is spherical interfaces which move superslowly towards the boundary without changing their shape. We show for the Cahn–Hilliard that the bubble drifts towards the closest point on the boundary provided it is sufficiently small. This is contrasted with the related mass conserving Allen–Cahn equation where size is not an issue.

Type
Papers
Information
European Journal of Applied Mathematics , Volume 15 , Issue 1 , February 2004 , pp. 103 - 124
Copyright
© 2004 Cambridge University Press