Existence and continuous dependence results in the dynamical theory of piezoelectricity
Ciarletta, Michele
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni, Tome 7 (1996), p. 59-66 / Harvested from Biblioteca Digitale Italiana di Matematica
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The paper is concerned with the dynamical theory of linear piezoelectricity. First, an existence theorem is derived. Then, the continuous dependence of the solutions upon the initial data and body forces is investigated.

Nell'ambito della teoria lineare dei processi dinamici dei materiali piezoelettrici, si studiano teoremi di esistenza e di dipendenza continua. 1. INTRODUCTION

Publié le : 1996-05-01
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     author = {Michele Ciarletta},
     title = {Existence and continuous dependence results in the dynamical theory of piezoelectricity},
     journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
     volume = {7},
     year = {1996},
     pages = {59-66},
     zbl = {0885.35132},
     mrnumber = {1437652},
     language = {en},
     url = {http://dml.mathdoc.fr/item/RLIN_1996_9_7_1_59_0}
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Ciarletta, Michele. Existence and continuous dependence results in the dynamical theory of piezoelectricity. Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni, Tome 7 (1996) pp. 59-66. http://gdmltest.u-ga.fr/item/RLIN_1996_9_7_1_59_0/

[1] Dokmeci, M. C., Recent advances: vibrations of piezoelectric crystals. Int. J. Engng. Sci., 18, 1980, 431-448. | Zbl 0439.73098

[2] Nowacki, W., Mathematical models of phenomenological piezoelectricity. In: O. Brulin - R. K. T. Hsieh (eds.), New Problems in Mechanics of Continua. University of Waterloo Press, Ontario 1983, 29. | Zbl 0564.73095

[3] Toupin, R. A., A dynamical theory of elastic dielectrics. Int. J. Engng. Sci., 1, 1963, 101-126. | MR 153286

[4] Eringen, A. C. - Dixon, R. C., A dynamical theory of polar elastic dielectrics. I, II. Int. J. Engng. Sci., 3, 1965, 359-398. | MR 187465

[5] Parkus, H., Magnetothermoelasticity. In: CISM Lectures Notes, Springer-Verlag, vol. 118, Berlin-Heidelberg-New York1972. | Zbl 0269.73069

[6] Grot, R. A., Relativiste continuum physics. Electromagnetic interactions. In: A. C. Eringen (ed.), Continuum Physics. Academic Press, vol. III, New York 1976. | MR 468445

[7] Maugin, A. G., Continuum Mechanics of Electromagnetic Solids. North-Holland, Amsterdam1987. | MR 954611 | Zbl 0652.73002

[8] Ieşan, D., Plane strain problems in piezoelectricity. Int. J. Engng. Sci., 25, 1987, 1511-1523. | MR 921364 | Zbl 0645.73017

[9] Ieşan, D., Reciprocity, uniqueness and minimum principles in the linear theory of piezoelectricity. Int. J. Engng. Sci., 28, 1990, 1139-1149. | MR 1083645 | Zbl 0718.73071

[10] Dafermos, C. M., Contraction semigroups and trend to equilibrium in continuum mechanics. In: P. Germain - B. Nayroles (eds.), Applications of Methods of Functional Analysis to Problems in Mechanics. Lecture Notes in Mathematics, vol. 503, Springer, Berlin 1976, 295-306. | Zbl 0345.47032

[11] Navarro, C. B. - Quintanilla, R., On existence and uniqueness in incremental thermoelasticity. ZAMP, 35, 1984, 206-215. | MR 756406 | Zbl 0549.73007

[12] Fichera, G., Existence theorems in elasticity. In: C. Truesdell (ed.), Flügge's Handbuch der Physik, vol. VIa/2, Springer-Verlag, Berlin-Heidelberg-New York 1972, 347-388. | Zbl 0277.73001

[13] Pazy, A., Semigroups of Linear Operators and Applications to Partial Differential Equations. Springer-Verlag, New York-Berlin-Heidelberg-Tokyo1983. | MR 710486 | Zbl 0516.47023

[14] Dafermos, C. M., The second law of thermodynamics and stability. Arch. Rational Mech. Anal., 70, 1979, 167-179. | MR 546634 | Zbl 0448.73004

[15] Beevers, C. E. - Craine, R. E., On the thermodynamics and stability of deformable dielectrics. Appl. Sci. Res., 37, 1981, 241-256. | MR 641088 | Zbl 0493.73091