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A mathematical analysis of a nonisothermal Allen–Cahn type system: error estimates
Author(s) -
Vaz C. L. D.,
Boldrini J. L.
Publication year - 2012
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.2505
Subject(s) - mathematics , allen–cahn equation , eigenvalues and eigenvectors , type (biology) , operator (biology) , laplace operator , galerkin method , binary number , inverse , mathematical analysis , finite element method , thermodynamics , geometry , quantum mechanics , gene , transcription factor , biology , ecology , biochemistry , chemistry , physics , arithmetic , repressor
In this article, under certain conditions, we prove the regularity for the solutions of an Allen–Cahn phase‐field type system obtained as limits of approximate solutions constructed by using a semidiscrete spectral Galerkin method. With the help of this improved regularity, as one compares to previous results, we then derive error estimates for the approximate solutions in terms of the inverse of the eigenvalues of the Laplacian operator. The system under investigation may model the evolution of solidification or melting of certain binary alloys. Copyright © 2012 John Wiley & Sons, Ltd.