Unique global solvability of the Fried-Gurtin model for phase transitions in solids
Keywords
Allen-Cahn equation, elasticity, phase transitions, existence and uniquenessAbstract
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.Downloads
Published
2004-12-01
How to Cite
1.
KOSOWSKI, Zenon and PAWŁOW, Irena. Unique global solvability of the Fried-Gurtin model for phase transitions in solids. Topological Methods in Nonlinear Analysis. Online. 1 December 2004. Vol. 24, no. 2, pp. 209 - 237. [Accessed 29 March 2024].
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