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Local solutions to a model of piezoelectric materials
Author(s) -
Hamdache Kamel,
Hamroun Djamila
Publication year - 2004
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.519
Subject(s) - piezoelectricity , mathematics , displacement (psychology) , dipole , mathematical analysis , heat equation , electric displacement field , electric dipole moment , time domain , wave equation , domain (mathematical analysis) , physics , acoustics , computer science , quantum mechanics , psychology , computer vision , psychotherapist
A local existence theorem is proved for a non‐linear coupled system modelling the electromechanical motion of a one‐dimensional piezoelectric body with domain switching. The system is composed by a heat equation describing the behaviour of the number of electric dipoles and by a wave equation governing the dynamic of the electric displacement. The main coupling in the system appears in the time‐dependent velocity of the waves depending on the number of electric dipoles. The proof of the result relies on a time decay estimate satisfied by the number of electric dipoles and an uniform estimate of the solution of the regularized wave equation. Copyright © 2004 John Wiley & Sons, Ltd.