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1991 | 54 | 2 | 135-145
Tytuł artykułu

$L^p$-$L^q$-Time decay estimate for solution of the Cauchy problem for hyperbolic partial differential equations of linear thermoelasticity

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Abstrakty
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We prove the $L^p$-$L^q$-time decay estimates for the solution of the Cauchy problem for the hyperbolic system of partial differential equations of linear thermoelasticity. In our proof based on the matrix of fundamental solutions to the system we use Strauss-Klainerman's approach [12], [5] to the $L^p$-$L^q$-time decay estimates.
Twórcy
  • Department of Mathematics, Military Technical Academy, S. Kaliskiego 2, 01-489 Warszawa, Poland
Bibliografia
  • [1] R. Adams, Sobolev Spaces, Academic Press, New York 1975.
  • [2] K. O. Friedrichs, Symmetric hyperbolic linear differential equations, Comm. Pure Appl. Math. 7 (1954), 345-392.
  • [3] Yu. V. Egorov, Linear Differential Equations of Principal Type, Nauka, Moscow 1984 (in Russian).
  • [4] J. Gawinecki, Matrix of fundamental solutions for the system of equations of hyperbolic thermoelasticity with two relaxation times and solution of the Cauchy problem, Bull. Acad. Polon. Sci., Sér. Sci. Techn. 1988 (in print).
  • [5] S. Klainerman, Global existence for nonlinear wave equations, Comm. Pure Appl. Math. 33 (1980), 43-101.
  • [6] S. Klainerman, Long-time behaviour of solutions to nonlinear evolution equations, Arch. Rational Mech. Anal. 78 (1982), 72-98.
  • [7] S. Klainerman and G. Ponce, Global, small amplitude solutions to nonlinear evolution equations, Comm. Pure Appl. Math. 36 (1983), 133-141.
  • [8] J. L. Lions et E. Magenes, Problèmes aux limites non homogènes et applications, Dunod, Paris 1968.
  • [9] A. Piskorek, Fourier and Laplace transformation with their applications, Warsaw University, 1988 (in Polish).
  • [10] J. Shatah, Global existence of small solutions to nonlinear evolution equations, J. Differential Equations 46 (1982), 409-425.
  • [11] S. L. Sobolev, Applications of Functional Analysis in Mathematical Physics, 3th ed. Nauka, Moscow 1988 (in Russian).
  • [12] W. A. Strauss, Nonlinear scattering theory at low energy, J. Funct. Anal. 41 (1981), 110-113.
  • [13] E. S. Suhubi, Thermoelastic solids, in: Continuum Physics, A. C. Eringen (ed.), Academic Press, New York 1975.
  • [14] H. Triebel, Interpolation Theory, Function Spaces, Differential Operators, Deutscher Verlag der Wissenschaften, Berlin 1978.
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bwmeta1.element.bwnjournal-article-apmv54z2p135bwm
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