### Abstract

Original language | English |
---|---|

Pages (from-to) | 4375-4384 |

Number of pages | 12 |

Journal | Mathematical Methods in the Applied Sciences |

Volume | 39 |

Issue number | 15 |

Early online date | 18 Feb 2016 |

DOIs | |

Publication status | Published - 31 Oct 2016 |

### Fingerprint

### Keywords

- piezo-electric ultrasonic transducers
- magneto-electro-thermo-elastic problem
- quasi-electrostatic case
- sensor
- mathematical modelling

### Cite this

*Mathematical Methods in the Applied Sciences*,

*39*(15), 4375-4384. https://doi.org/10.1002/mma.3866

}

*Mathematical Methods in the Applied Sciences*, vol. 39, no. 15, pp. 4375-4384. https://doi.org/10.1002/mma.3866

**On well-posedness for some thermo-piezoelectric coupling models.** / Mulholland, Anthony J.; Picard, Rainer; Trostorff, Sascha; Waurick, Marcus.

Research output: Contribution to journal › Article

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

VL - 39

SP - 4375

EP - 4384

JO - Mathematical Methods in the Applied Sciences

JF - Mathematical Methods in the Applied Sciences

SN - 0170-4214

IS - 15

ER -