Electron. J. Diff. Equ.,
Vol. 2010(2010), No. 120, pp. 119.
Nonlinear boundary dissipation for a coupled system
of KleinGordon equations
Aldo T. Louredo, M. Milla Miranda
Abstract:
This article concerns the existence of
solutions and the decay of the energy of the mixed problem
for the coupled system of KleinGordon equations
with the nonlinear boundary conditions,
and boundary conditions
on
, where
is a bounded open set of
,
a real number,
a subset of the boundary
of
and
a real function defined on
.
Assuming that each
is strongly monotone in the second
variable, the existence of global solutions of the mixed problem
is obtained. For that it is used the Galerkin method, the Strauss'
approximations of real functions and trace theorems for nonsmooth
functions. The exponential decay of the energy for a particular
stabilizer is derived by application of a Lyapunov functional.
Submitted August 3, 2009. Published August 24, 2010.
Math Subject Classifications: 35L70, 35L20, 35L05.
Key Words: Galerkin method; special basis; boundary stabilization.
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Aldo T. Lourêdo
Universidade Estadual da Paraíba, DME
CEP 58109095  Campina Grande  PB, Brazil
email: aldotl@bol.com.br 

M. Milla Miranda
Universidade Federal do Rio de Janeiro  IM
CEP 21945970  Rio de Janeiro  RJ, Brazil
email: milla@im.ufrj.br

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