Asymptotic behavior of solution of hyperbolic problems on a cylindrical domain

Pages: 160 - 169, Issue Special, September 2007

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Bernard Brighi - Université de Haute Alsace, Laboratoire de mathématiques, F.S.T., 4 rue des frères Lumière, 68093 MULHOUSE, France (email)
S. Guesmia - Université de Haute Alsace, Laboratoire Mathématiques, Informatique et Applications, 4, rue des Frères Lumière, 68093 Mulhouse Cedex, France (email)

Abstract: The asymptotic behavior of the hyperbolic evolution problems of order two, on a cylindrical domain $\Omega$ = $\Delta \times \omega$, with coefficients dependent on a parameter is examined. The convergence of the solution of such problems towards a solution of a problem of the same type defined in $\omega$ is proved, and the rate of convergence estimates is given. One can see this work as a singular perturbation of the hyperbolic problems in some directions.

Keywords:  Hyperbolic problems, asymptotic behavior, singular perturbations.
Mathematics Subject Classification:  Primary: 35L15, 35L20, 35B40, 35B25.

Received: September 2006;      Revised: December 2006;      Published: September 2007.