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doubly nonlinear differential inclusions

European Journal of Applied Mathematics (1)

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Existence results for diffuse interface models describing phase separation and damage *
CHRISTIAN HEINEMANN, CHRISTIANE KRAUS
Journal:

European Journal of Applied Mathematics / Volume 24 / Issue 2 / April 2013

Published online by Cambridge University Press:

09 November 2012, pp. 179-211
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In this paper, we analytically investigate multi-component Cahn–Hilliard and Allen–Cahn systems which are coupled with elasticity and uni-directional damage processes. The free energy of the system is of the form ∫Ω½Γ∇c : ∇c + ½|∇z|2+Wch(c)+Wel(e,c,z)dx with a polynomial or logarithmic chemical energy density Wch, an inhomogeneous elastic energy density Wel and a quadratic structure of the gradient of damage variable z. For the corresponding elastic Cahn–Hilliard and Allen–Cahn systems coupled with uni-directional damage processes, we present an appropriate notion of weak solutions and prove existence results based on certain regularization methods and a higher integrability result for strain e.

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Existence results for diffuse interface models describing phase separation and damage *

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Existence results for diffuse interface models describing phase separation and damage*

Existence results for diffuse interface models describing phase separation and damage *