IJPAM: Volume 29, No. 4 (2006)

GLOBAL EXISTENCE FOR A QUASILINEAR HYPERBOLIC
EQUATION IN A NONCYLINDRICAL DOMAIN

J. Ferreira$^1$, C.A. Raposo$^2$, M.L. Santos$^3$
$^{1,2}$Departamento de Matemática
Universidade Federal de São João del-Rei
Praça Frei Orlando, 170, CEP: 36307-352
São João del-Rei, MG, BRAZIL
$^1$e-mail: jf@ufsj.edu.br
$^2$e-mail: raposo@ufsj.edu.br
$^3$Departamento de Matemática
Universidade Federal do Pará
CEP: 66075-110 Belém, PA, BRAZIL
and
IESAM-Instituto de Estudos Superiores da Amazônia
Av. Governador José Malcher
1148, Belém, PA, BRAZIL
e-mail: ls@ufpa.br


Abstract.We study the existence of a weak global solution of the mixed problem to the quasilinear hyperbolic equation

\begin{displaymath}
u_{tt}-\text{\rm div}\,(\vert\nabla u\vert^{p-2}\nabla u)-\triangle u_t=f(t,x)\eqno{(1)}
\end{displaymath}

is a noncylindrical domain. Our proof is based on a penalty argument by J.L. Lions and Galerkin approximations.

Received: May 13, 2006

AMS Subject Classification: 35L70

Key Words and Phrases: quasilinear equation, global solution, penalty method, noncylindrical domain

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2006
Volume: 29
Issue: 4