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On well‐posedness for some thermo‐piezoelectric coupling models
Author(s) -
Mulholland Anthony J.,
Picard Rainer,
Trostorff Sascha,
Waurick Marcus
Publication year - 2016
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.3866
Subject(s) - piezoelectricity , coupling (piping) , envelope (radar) , inverse , mathematics , ultrasonic sensor , class (philosophy) , inverse problem , mathematical optimization , computer science , calculus (dental) , mechanical engineering , acoustics , mathematical analysis , engineering , physics , telecommunications , geometry , artificial intelligence , medicine , dentistry , radar
There is an increasing reliance on mathematical modelling to assist in the design of piezoelectric ultrasonic transducers since this provides a cost‐effective and quick way to arrive at a first prototype. Given a desired operating envelope for the sensor, the inverse problem of obtaining the associated design parameters within the model can be considered. It is therefore of practical interest to examine the well‐posedness of such models. There is a need to extend the use of such sensors into high‐temperature environments, and so this paper shows, for a broad class of models, the well‐posedness of the magneto‐electro‐thermo‐elastic problem. Because of its widespread use in the literature, we also show the well‐posedness of the quasi‐electrostatic case. Copyright © 2016 John Wiley & Sons, Ltd.