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Spatial decay for several phase‐field models
Author(s) -
Miranville A.,
Quintanilla R.
Publication year - 2013
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201200131
Subject(s) - exponential decay , exponential function , isothermal process , field (mathematics) , phase (matter) , fourier transform , statistical physics , phase field models , cahn–hilliard equation , physics , mathematics , mathematical analysis , thermodynamics , partial differential equation , quantum mechanics , pure mathematics
Abstract In this paper, we study the spatial behavior of three phase‐field models. First, we consider the Cahn‐Hilliard equation and we obtain the exponential decay of solutions under suitable assumptions on the data. Then, for the classical isothermal phase‐field equation (i.e., the Allen‐Cahn equation), we prove the nonexistence and the fast decay of solutions and, for the nonisothermal case governed by the Fourier law, we obtain a Phragmén‐Lindelöf alternative of exponential type, respectively.