Topological Methods in Nonlinear Analysis
- Topol. Methods Nonlinear Anal.
- Volume 24, Number 2 (2004), 209-237.
Unique global solvability of the Fried-Gurtin model for phase transitions in solids
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.
Topol. Methods Nonlinear Anal., Volume 24, Number 2 (2004), 209-237.
First available in Project Euclid: 23 June 2016
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Kosowski, Zenon; Pawłow, Irena. Unique global solvability of the Fried-Gurtin model for phase transitions in solids. Topol. Methods Nonlinear Anal. 24 (2004), no. 2, 209--237. https://projecteuclid.org/euclid.tmna/1466704917