35K35 Initial-boundary value problems for higher-order parabolic equations
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A typical phase field approach for describing phase separation and
coarsening phenomena in alloys is the Cahn-Hilliard model. This
model has been generalized to the so-called Cahn-Larche system
by combining it with elasticity to capture non-neglecting deformation
phenomena,
which occur during phase separation and coarsening processes in the material.
In order to account for damage effects,
we extend the existing framework of Cahn-Hilliard and Cahn-Larche
systems by incorporating an internal damage variable of local character. This
damage variable allows to model the effect that damage of a material point is influenced by its local surrounding.
The damage process is described by a unidirectional rate-dependent evolution inclusion
for the internal variable.
For the introduced Cahn-Larche systems
coupled with rate-dependent
damage processes, we
establish a suitable notion of weak solutions and prove existence of weak solutions.