TY - JOUR
T1 - On well-posedness for some thermo-piezoelectric coupling models
AU - Mulholland, Anthony J.
AU - Picard, Rainer
AU - Trostorff, Sascha
AU - Waurick, Marcus
N1 - This is the peer reviewed version of the following article: Mulholland, A. J., Picard, R., Trostorff, S., & Waurick, M. (2016). On well-posedness for some thermo-piezoelectric coupling models. Mathematical Methods in the Applied Sciences, 39(15), 4375-4384., which has been published in final form at http://dx.doi.org/10.1002/mma.3866. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.
PY - 2016/10/31
Y1 - 2016/10/31
N2 - 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. Due to its widespread use in the literature, we also show the well-posedness of the quasi-electrostatic case.
AB - 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. Due to its widespread use in the literature, we also show the well-posedness of the quasi-electrostatic case.
KW - piezo-electric ultrasonic transducers
KW - magneto-electro-thermo-elastic problem
KW - quasi-electrostatic case
KW - sensor
KW - mathematical modelling
UR - http://onlinelibrary.wiley.com/wol1/doi/10.1002/mma.3866/full
U2 - 10.1002/mma.3866
DO - 10.1002/mma.3866
M3 - Article
SN - 0170-4214
VL - 39
SP - 4375
EP - 4384
JO - Mathematical Methods in the Applied Sciences
JF - Mathematical Methods in the Applied Sciences
IS - 15
ER -