Thanh Long Nguyen, Tien Dung Bui
Abstract:
We consider the initial-boundary value problem for the
nonlinear wave equation
where
are given functions, the unknown function
and the unknown boundary value
satisfy the nonlinear integral equation
where
,
,
are given functions. We prove the existence
and uniqueness of weak solutions to this problem, and discuss
the stability of the solution with respect to the functions
,
, and
.
For the proof, we use the Galerkin method.
Submitted January 14, 2004. Published September 3, 2004.
Math Subject Classifications: 35B30, 35L70, 35Q72.
Key Words: Galerkin method; integrodifferential equations;
Schauder fixed point theorem; weak solutions;
stability of the solutions
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Thanh Long Nguyen Department of Mathematics and Computer Science University of Natural Science Vietnam National University HoChiMinh City 227 Nguyen Van Cu Str., Dist.5, HoChiMinh City, Vietnam email: longnt@hcmc.netnam.vn |
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Tien Dung Bui Department of Mathematics University of Architecture of HoChiMinh City 196 Pasteur Str., Dist. 3, HoChiMinh City, Vietnam |
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