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Global solutions in one-dimensional magneto-thermoviscoelasticity

Published online by Cambridge University Press:  16 July 2009

Jürgen Sprekels
Jürgen Sprekels
Affiliation:
Fachbereich 10 Bauwesen, Universität-GH Essen, Postfach 10 37 64, D-4300 Essen 1, Germany
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Abstract

Global smooth solutions are shown to exist for the system governing magneto-thermoviscoelastic phenomena in an electrically and thermally conducting isotropic solid immersed in an electromagnetic field. It is assumed that displacement currents are negligible, and that all field quantities depend on one space variable only; Joule heating is included.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 2 , Issue 1 , March 1991 , pp. 83 - 96
Copyright
Copyright © Cambridge University Press 1991

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References

Andrews, G. 1980 On the existence of solutions to the equation utt = uxxt+π(ux)x. J. Diff. Eqns. 35, 200–231.CrossRefGoogle Scholar
Dafermos, C. M. 1982 Global smooth solutions to the initial boundary value problem for the equations of one-dimensional thermoviscoelasticity. SIAM J. Math. Anal. 13, 397–408.CrossRefGoogle Scholar
Landau, L. D., Lifshitz, E. M. & Pitaevskii, L. P. 1984 Electrodynamics of Continuous Media, 2nd ed., Pergamon Press.Google Scholar
Ladyzenskaya, O. A., Solonntkov, V. A. & Uralceva, N. N. 1968 Linear and Quasilinear Equations of Parabolic Type. Amer. Math. Soc.Google Scholar
Maugin, G. A. 1988 Continuum Mechanics of Electromagnetic Solids. North-Holland.Google Scholar
Paria, G. 1962 On magneto-thermo-elastic plane waves. Proc. Cambridge Phil. Soc. 58, 527–531.CrossRefGoogle Scholar
Pego, R. L. 1986 Phase transitions: stability and admissibility in one-dimensional nonlinear viscoelasticity. Preprint. No. 180 IMA, University of Minnesota.Google Scholar
Rogers, R. C. & Antman, S. S. 1986 Steady-state problems of nonlinear electro-magneto-thermoelasticity. Arch. Rat. Mech. Anal. 95, 279–323.CrossRefGoogle Scholar
Valenti, A. 1988 The asymptotic analyses of non-linear waves in magneto-thermoelastic solids with thermal relaxation. ZAMP 39, 299–311.Google Scholar