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Classical solvability of 1‐D Cahn–Hilliard equation coupled with elasticity
Author(s) -
Pawłow Irena,
Zaja̧czkowski Wojciech M.
Publication year - 2006
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.715
Subject(s) - cahn–hilliard equation , mathematics , elasticity (physics) , mathematical analysis , nonlinear system , binary number , fixed point theorem , partial differential equation , thermodynamics , physics , arithmetic , quantum mechanics
In this paper, we prove the classical solvability of a nonlinear 1‐D system of hyperbolic–parabolic type arising as a model of phase separation in deformable binary alloys. The system is governed by the nonstationary elasticity equation coupled with the Cahn–Hilliard equation. The existence proof is based on the application of the Leray–Schauder fixed point theorem and standard energy methods. Copyright © 2006 John Wiley & Sons, Ltd.