Existence and continuous dependence results in the dynamical theory of piezoelectricity

Michele Ciarletta

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1996)

  • Volume: 7, Issue: 1, page 59-66
  • ISSN: 1120-6330

Abstract

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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.

How to cite

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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 7.1 (1996): 59-66. <http://eudml.org/doc/244179>.

@article{Ciarletta1996,
abstract = {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.},
author = {Ciarletta, Michele},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Piezoelectricity; Dynamical; Existence; Stability; displacement field; linear piezoelectricity; Maxwell equations; strain field; dissipative boundary conditions; semigroup theory},
language = {eng},
month = {5},
number = {1},
pages = {59-66},
publisher = {Accademia Nazionale dei Lincei},
title = {Existence and continuous dependence results in the dynamical theory of piezoelectricity},
url = {http://eudml.org/doc/244179},
volume = {7},
year = {1996},
}

TY - JOUR
AU - Ciarletta, Michele
TI - Existence and continuous dependence results in the dynamical theory of piezoelectricity
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1996/5//
PB - Accademia Nazionale dei Lincei
VL - 7
IS - 1
SP - 59
EP - 66
AB - 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.
LA - eng
KW - Piezoelectricity; Dynamical; Existence; Stability; displacement field; linear piezoelectricity; Maxwell equations; strain field; dissipative boundary conditions; semigroup theory
UR - http://eudml.org/doc/244179
ER -

References

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  1. DOKMECI, M. C., Recent advances: vibrations of piezoelectric crystals. Int. J. Engng. Sci., 18, 1980, 431-448. Zbl0439.73098
  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, Ontario1983, 29. Zbl0564.73095
  3. TOUPIN, R. A., A dynamical theory of elastic dielectrics. Int. J. Engng. Sci., 1, 1963, 101-126. MR153286
  4. ERINGEN, A. C. - DIXON, R. C., A dynamical theory of polar elastic dielectrics. I, II. Int. J. Engng. Sci., 3, 1965, 359-398. MR187465
  5. PARKUS, H., Magnetothermoelasticity. In: CISM Lectures Notes, Springer-Verlag, vol. 118, Berlin-Heidelberg-New York1972. Zbl0269.73069
  6. GROT, R. A., Relativiste continuum physics. Electromagnetic interactions. In: A. C. ERINGEN (ed.), Continuum Physics. Academic Press, vol. III, New York1976. MR468445
  7. MAUGIN, A. G., Continuum Mechanics of Electromagnetic Solids. North-Holland, Amsterdam1987. Zbl0652.73002MR954611
  8. IEŞAN, D., Plane strain problems in piezoelectricity. Int. J. Engng. Sci., 25, 1987, 1511-1523. Zbl0645.73017MR921364DOI10.1016/0020-7225(87)90029-2
  9. IEŞAN, D., Reciprocity, uniqueness and minimum principles in the linear theory of piezoelectricity. Int. J. Engng. Sci., 28, 1990, 1139-1149. Zbl0718.73071MR1083645DOI10.1016/0020-7225(90)90113-W
  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, Berlin1976, 295-306. Zbl0345.47032
  11. NAVARRO, C. B. - QUINTANILLA, R., On existence and uniqueness in incremental thermoelasticity. ZAMP, 35, 1984, 206-215. Zbl0549.73007MR756406DOI10.1007/BF00947933
  12. FICHERA, G., Existence theorems in elasticity. In: C. TRUESDELL (ed.), Flügge's Handbuch der Physik, vol. VIa/2, Springer-Verlag, Berlin-Heidelberg-New York1972, 347-388. Zbl0277.73001
  13. PAZY, A., Semigroups of Linear Operators and Applications to Partial Differential Equations. Springer-Verlag, New York-Berlin-Heidelberg-Tokyo1983. Zbl0516.47023MR710486DOI10.1007/978-1-4612-5561-1
  14. DAFERMOS, C. M., The second law of thermodynamics and stability. Arch. Rational Mech. Anal., 70, 1979, 167-179. Zbl0448.73004MR546634DOI10.1007/BF00250353
  15. BEEVERS, C. E. - CRAINE, R. E., On the thermodynamics and stability of deformable dielectrics. Appl. Sci. Res., 37, 1981, 241-256. Zbl0493.73091MR641088DOI10.1007/BF00951250

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