Abstract
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.
Citation
Zenon Kosowski. Irena Pawłow. "Unique global solvability of the Fried-Gurtin model for phase transitions in solids." Topol. Methods Nonlinear Anal. 24 (2) 209 - 237, 2004.
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