Geodesic
Existence and boundary stabilization of a nonlinear hyperbolic equation with time-dependent coefficients
Electronic Journal of Differential Equations, Tome 1998 (1998).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: In this article, we study the hyperbolic problem $$ K(x,t)u_{tt} - \sum_{j=1}^n\left(a(x,t)u_{x_j}\right) + F(x,t,u,\nabla u) = 0 $$ coupled with boundary conditions $$u=0,\quad\hbox{on }\Gamma_1\,, \quad {\partial u \over\partial\nu} + \beta(x)u_t =0\quad\hbox{ on }\Gamma_0\,.$$ Here the variable $x$ belongs to a bounded region of ${\Bbb R}^n$, whose boundary is partitioned into two disjoint sets $\Gamma_0,\Gamma_1$. We prove existence, uniqueness, and uniform stability of strong and weak solutions when the coefficients and the boundary conditions provide a damping effect.
Classification : 35B40, 35L80
Keywords: boundary stabilization, asymptotic behaviour 
@article{EJDE_1998__1998__a21,
     author = {Cavalcanti, M.M. and Domingos Cavalcanti, V.N. and Soriano, J.A.},
     title = {Existence and boundary stabilization of a nonlinear hyperbolic equation with time-dependent coefficients},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {1998},
     year = {1998},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_1998__1998__a21/}
}
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Cavalcanti, M.M.; Domingos Cavalcanti, V.N.; Soriano, J.A. Existence and boundary stabilization of a nonlinear hyperbolic equation with time-dependent coefficients. Electronic Journal of Differential Equations, Tome 1998 (1998). http://geodesic.mathdoc.fr/item/EJDE_1998__1998__a21/