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End effects in the dynamical problem of magneto-elasticity

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Języki publikacji
EN
Abstrakty
EN
In this paper we derive spatial decay bounds for the solutions of the linear dynamical problem of magneto-elasticity in a semi-infinite cylindrical region. For the forward-in-time problem we prove that an energy expression is bounded from above by a decaying exponential of a quadratic polynomial of the distance. We derive a spatial decay estimate for the backward-in-time problem as well. The proof works only if the cross-section is a finite union of rectangles with axes parallels to Ox2 and Ox3. As a conclusion we consider the extension of the preceding bound to the heat conduction case.
Rocznik
Strony
245--256
Opis fizyczny
Bibliogr. 22 poz.
Twórcy
  • Matematica Aplicada 2 Universidad Politecnica de Catalunya, Colon, 11. Terrassa. Barcelona. Spain, ramon@ma2.upc.es
Bibliografia
  • 1. K. A. AMES and B. STRAUGHAN, Non-standard and improperly posed problems, Academic Press, San Diego 1997.
  • 2. E. ANDREOU and G. DASSION, Dissipation of energy for magnetoelastic waves in a conductive medium, Quart. Appl. Math., 55, 23-39, 1997.
  • 3. F. BOFILL and R. QUINTANILLA, On a backward in time problem arising in viscoelasticity, Mathematics and numerical aspects of wave propagation, A.BERMUDEZ, D. GÓMEZ, C. HAZARD, P. JOLY and J. E. ROBERTS, [Eds.] SIAM 123-127, 2000.
  • 4. S. CHANDLER, Phase velocity and energy loss in magneto-thermo-elastic waves, Int. Jour. Eng, Sci., 6, 409-424, 1968.
  • 5. C. A. ERINGEN and G. A. MAUGIN, Electrodynamics of continua I, Springer-Verlag, New- York 1990.
  • 6. F. FRANCHI and B. STRAUGHAN, Spatial decay estimates and continuous dependence for an equation from dynamo theory, Proc. Royal Society London A, 445, 437-451, 1984.
  • 7. C. O. HORGAN, Recent developments concerning Saint-Venant’s Principle: An update, Applied Mechanics Reviews, 42, 295-303, 1989.
  • 8. C.O. HORGAN, Recent developments concerning Saint-Venant’s Principle: A second update, Applied Mechanics Reviews, 49, 101-111, 1996.
  • 9. C. O. HORGAN and J.K. KNOELES, Recent developments concerning Saint- Venant’s Principle, Advances in Applied Mechanics, J. W. HUTCHINSIN and T. Y. WU, [Eds.J 23 Academic Press pp. 179-269, New York 1983.
  • 10. C. O. HORGAN, L. E. PAYNE and L.T. WHEELER, Spatial decay estimates in transient heat conduction, Quart. Appl. Math., 42, 119-127, 1984.
  • 11. C. O. HORGAN and R. QUINTANILLA, Spatial decay of transient end effects in functionally graded heat conducting materials, Quat. Appl. Math., XIL, 529-542, 2001.
  • 12. C. LIN and L. PAYNE, On the spatial decay of ill-posed parabolic problems, Math. Models and Methods in Applied Science, 3, 563-575, 1993.
  • 13. J.E. MUNOZ RIVERA and R. RACKE, Magento-thermo-elasticity; Large-time behavior for linear systems, Advances in Differential Equations, 6, 359-384, 2001.
  • 14. J. E. MUNOZ RIVERA and R. RACKE, Polynomial stability in two-dimensional magnetoelasticity, Universitat Konstanz, 117, 2000.
  • 15. G. PARIA, Magneto-elasticity and magneto-thermo-elasticity, Advances in Appl. Mechanics, 10, 73-112, 1967.
  • 16. G. PERLA MENZALA and E. ZUAZUA, Energy decay of magnetoelastic waves in a bounded conductive medium, Asymptotic Analysis, 18, 349-362, 1998.
  • 17. R. QUINTANILLA, End effects in thermoelasticity, Mathematical Methods in Applied Sciences, 24, 93-102, 2001.
  • 18. R. QUINTANILLA, Damping of end effects in a thermoelastic theory, Applied Mathematics Letters, 14, 137-141, 2001.
  • 19. R. QUINTANILLA, On the spatial decay for the dynamical problem of thermo-microstretch elastic solids, Int. J. Engng. Sci., 40, 109-121, 2002.
  • 20. R. QUINTANILLA, Spatial asymptotic behaviour in incremental thermoelasticity, Asympt. Anal., 27, 265-279, 2001.
  • 21. R. QUINTANILLA, Comparison arguments in nonlinear viscoelasticity, Manuscript 2001.
  • 22. A.J. WILSON, The propagation of magneto-thermo-elastic plane waves, Proc. Camb. Phil. Soc., 59. 483-488, 1963.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BAT4-0005-0095
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