IJPAM: Volume 70, No. 3 (2011)

HYPERBOLIC EQUATION WITH A RESISTANCE TERM
IN A NONCYLINDRICAL DOMAIN

G.O. Antunes$^1$, P.N. da Silva$^2$, R.S. Busse$^3$
$^{1,3}$Department of Mathematics and Statistics
UNIRIO - Universidade Federal do Estado do Rio de Janeiro
458, Pasteur Av., 296, Urca, Cep 22290-240
Rio de Janeiro, RJ, BRAZIL
$^2$Departament of Mathematical Analysis
UERJ - Universidade do Estado do Rio de Janeiro
524, São Francisco Xavier St., 20559-900, Rio de Janeiro, RJ, BRAZIL


Abstract. In this paper we investigate the existence and uniqueness of solution for the equation $u^{\prime\prime}-\Delta u=-\nabla p$ in a noncylindrical domain $\widehat{Q}$, with div $u=0$ in $\widehat{Q}$, under some initial and boundary conditions. This model, in a cylindrical domain, was originally proposed by J.L. Lions and it is related to the dynamics elasticity for incompressible materials.

Received: January 17, 2011

AMS Subject Classification: 35L20, 35L65

Key Words and Phrases: hyperbolic equation, noncylindrical domain, Galerkin method

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2011
Volume: 70
Issue: 3