On the existence and the asymptotic stability of solutions to the equations of linear thermoelasticity (original) (raw)

1968, Archive For Rational Mechanics And Analysis

Abstract

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The paper investigates the existence and asymptotic stability of solutions to linear thermoelastic equations under homogeneous boundary conditions. It builds upon previous work in the field, acknowledging essential contributions and conjectures made by various researchers. The findings aim to enhance the understanding of free vibrations in elastic bodies modeled by thermoelasticity, ultimately providing insights into stability conditions necessary for such systems.

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References (21)

  1. ZENER, C., Phys. Rev. 52, 230--235 (1937); 53, 90--99 (1938).
  2. PXSLER, M., Z. Physik 122, 357--386 (1944).
  3. ALBLAS, J. B., Appl. Sci. Res. (A) 10, 349--362 (1961).
  4. CHADWICK, P., Mathematika 9, 38--48 (1962).
  5. ERICKSEN, J. L., Intemat. J. Solids and Structures 2, 573--580 (1966).
  6. ERICI~SEN, J. L., Proc. Fifth U.S. Nat. Congr. Appl. Mech. 187--193 (1966).
  7. LIONS, J. L., ]~quations Diff6rentielles-Op6rationnelles et probl6mes aux limites. Berlin- G6ttingen-Heidelberg: Springer 1961.
  8. WEINER, J. H., Quart. Appl. Math. 15, 102--105 (1957).
  9. IONESCU-CAzIMIR, V., Bull. Acad. Polon. Sci. S6r. Sci. Tech. 12, 565--579 (1964).
  10. AOMON, S., Lectures on Elliptic Boundary Value Problems. Princeton: Van Nostrand 1965.
  11. FICHERA, G., Lectures on Linear Elliptic Differential Systems and Eigenvalue Problems. Berlin-G6ttingen-Heidelberg: Springer 1965.
  12. FRIEDRICHS, K. O., Ann. of Math. 48, 441--471 (1947).
  13. TRUESDELL, C., d~ W. NOLL, The Non-Linear Field Theories of Mechanics. Berlin- Gbttingen-Heidelberg: Springer 1965.
  14. SOBOLEV, S. L., Some Applications of Functional Analysis in Mathematical Physics. Lenin- grad 1950. English translation by F. BROWDER; Providence: A. M.S. 1963.
  15. VI~IK, M. I., & O. A. LADY~ENSKAYA, Uspehi Mat. Nauk (N.S.), 11, no. 6 (72), 41--97 (1956). English translation in A. M. S. translations, Ser 2, 10, 223 --281 (1958).
  16. AGMON, S., DOUGLIS, A. & L. NIRENBERG, Comm. Pure Appl. Math. 12, 623--727 (1959); 17, 35--92 (1964).
  17. MORREY, C. B., Jr., Multiple Integrals in the Calculus of Variations. Berlin-G6ttingen- Heidelberg: Springer 1966.
  18. SHIELD, R. Z., Z. Angew. Math. Phys. 16, 649--686 (1965).
  19. ACHENBACH, J. D., Acta Mech. 3, 342--351 (1967).
  20. BOCHNER, S., Proc. Nat. Acad. Sci. U.S.A. 46, 1233--1236 (1960).
  21. LIONS, J. L., & P. A. RAVlART, ICC Bull. 5, 1 --21 (1966). Department of Mechanics The Johns Hopkins University Baltimore, Maryland (Received November 14, 1967)