Local solutions to a model of piezoelectric materials

✍ Scribed by Kamel Hamdache; Djamila Hamroun

• Book ID: 102512050
• Publisher: John Wiley and Sons
• Year: 2004
• Tongue: English
• Weight: 146 KB
• Volume: 27
• Category: Article
• ISSN: 0170-4214
• DOI: 10.1002/mma.519

✦ Synopsis

Abstract

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.