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Regularity and convergence results for a phase–field model with memory
Author(s) -
Bonfanti Giovanna,
Luterotti Fabio
Publication year - 1998
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/(sici)1099-1476(199808)21:12<1085::aid-mma986>3.0.co;2-6
Subject(s) - mathematics , uniqueness , convergence (economics) , mathematical analysis , neumann boundary condition , phase field models , boundary (topology) , boundary value problem , term (time) , field (mathematics) , heat flux , flux (metallurgy) , phase (matter) , pure mathematics , heat transfer , thermodynamics , physics , metallurgy , materials science , quantum mechanics , economics , economic growth
A phase–field model based on the Coleman–Gurtin heat flux law is considered. The resulting system of non‐linear parabolic equations, associated with a set of initial and Neumann boundary conditions, is studied. Existence, uniqueness, and regularity results are proved. An asymptotic analysis is also carried out, in the case where the coefficient of the interfacial energy term tends to 0. © 1998 B. G. Teubner Stuttgart—John Wiley & Sons, Ltd.