Premium
Metastable solutions for the thin‐interface limit of a p‐Laplacian phase field model
Author(s) -
JiménezCasas Ángela
Publication year - 2018
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.5197
Subject(s) - mathematics , metastability , generalization , laplace operator , limit (mathematics) , operator (biology) , phase (matter) , field (mathematics) , work (physics) , nonlinear system , mathematical physics , mathematical analysis , function (biology) , diffusion , phase field models , pure mathematics , physics , thermodynamics , quantum mechanics , biochemistry , chemistry , repressor , evolutionary biology , biology , transcription factor , gene
We consider a generalization of the semilinear phase field model from G. Caginalp), A. Jiménez‐Casas, and Rodriguez‐Bernal using a nonlinear diffusion operator (p‐Laplacian) for the phase field function. The main objective of this work is to prove the existence of the metastable solutions of the generalized system in the one‐dimensional case, which evolve very slowly in time.