Geodesic
Existence and boundary stabilization of a nonlinear hyperbolic equation with time-dependent coefficients
Electronic journal of differential equations, Tome 1998 (1998)
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},
     year = {1998},
     volume = {1998},
     zbl = {0892.35027},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_1998__1998__a21/}
}
TY  - JOUR
AU  - Cavalcanti,  M.M.
AU  - Domingos Cavalcanti,  V.N.
AU  - Soriano,  J.A.
TI  - Existence and boundary stabilization of a nonlinear hyperbolic equation with time-dependent coefficients
JO  - Electronic journal of differential equations
PY  - 1998
VL  - 1998
UR  - http://geodesic.mathdoc.fr/item/EJDE_1998__1998__a21/
LA  - en
ID  - EJDE_1998__1998__a21
ER  - 
%0 Journal Article
%A Cavalcanti,  M.M.
%A Domingos Cavalcanti,  V.N.
%A Soriano,  J.A.
%T Existence and boundary stabilization of a nonlinear hyperbolic equation with time-dependent coefficients
%J Electronic journal of differential equations
%D 1998
%V 1998
%U http://geodesic.mathdoc.fr/item/EJDE_1998__1998__a21/
%G en
%F EJDE_1998__1998__a21
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/