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Strong solvability of 3‐D Cahn–Hilliard system in elastic solids
Author(s) -
Pawłow Irena,
Zaja̧czkowski W. M.
Publication year - 2007
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.946
Subject(s) - mathematics , uniqueness , nonlinear system , cahn–hilliard equation , variable (mathematics) , work (physics) , mathematical analysis , type (biology) , boundary value problem , weak solution , boundary (topology) , mathematical economics , partial differential equation , thermodynamics , ecology , physics , quantum mechanics , biology
In this paper we prove the existence and uniqueness of a strong solution to a 3‐D model of phase separation in elastic solids. The model has the form of an initial‐boundary‐value problem for a nonlinear coupled system of hyperbolic–parabolic type. The key idea of the proof is based on the analysis of the system once‐ and twice differentiated with respect to time variable. The paper develops results of the previous work ( Top. Meth. Nonlin. Anal. , in press). Copyright © 2007 John Wiley & Sons, Ltd.