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2007, 2007(Special): 160-169. doi: 10.3934/proc.2007.2007.160

Asymptotic behavior of solution of hyperbolic problems on a cylindrical domain

Bernard Brighi 1, and  S. Guesmia 2,

1. 

Université de Haute Alsace, Laboratoire de mathématiques, F.S.T., 4 rue des frères Lumière, 68093 MULHOUSE
2. 

Université de Haute Alsace, Laboratoire Mathématiques, Informatique et Applications, 4, rue des Frères Lumière, 68093 Mulhouse Cedex, France

Received  September 2006 Revised  December 2006 Published  September 2007

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: singular perturbations., Hyperbolic problems, asymptotic behavior.
Mathematics Subject Classification: Primary: 35L15, 35L20, 35B40, 35B2.
Citation: Bernard Brighi, S. Guesmia. Asymptotic behavior of solution of hyperbolic problems on a cylindrical domain. Conference Publications, 2007, 2007 (Special) : 160-169. doi: 10.3934/proc.2007.2007.160
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