Unique global solvability of the Fried-Gurtin model for phase transitions in solids

Zenon Kosowski, Irena Pawłow

DOI: http://dx.doi.org/10.12775/TMNA.2004.026


The paper is concerned with the existence and uniqueness of solutions
to the Allen-Cahn equation coupled with elasticity.
The system represents a particular, simple version of the Fried-Gurtin model
for solid-solid transitions with phase characterized by an order parameter.

The system is studied with the help of the Leray-Schauder fixed point theorem.
The main tool applied in the existence proof is the solvability theory of
parabolic problems in anisotropic Sobolev spaces with mixed time-space norms.


Allen-Cahn equation; elasticity; phase transitions; existence and uniqueness

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