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On Cahn—Hilliard systems with elasticity

Published online by Cambridge University Press:  12 July 2007

Harald Garcke
Harald Garcke
Affiliation:
NWF I—Mathematik, 93040 Regensburg, Germany ([email protected])
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Abstract

Elastic effects can have a pronounced effect on the phase-separation process in solids. The classical Ginzburg—Landau energy can be modified to account for such elastic interactions. The evolution of the system is then governed by diffusion equations for the concentrations of the alloy components and by a quasi-static equilibrium for the mechanical part. The resulting system of equations is elliptic-parabolic and can be understood as a generalization of the Cahn—Hilliard equation. In this paper we give a derivation of the system and prove an existence and uniqueness result for it.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 133 , Issue 2 , April 2003 , pp. 307 - 331
Copyright
Copyright © Royal Society of Edinburgh 2003

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