Thanh Long Nguyen, Tien Dung Bui
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
| Tien Dung Bui |
Department of Mathematics
University of Architecture of HoChiMinh City
196 Pasteur Str., Dist. 3, HoChiMinh City, Vietnam
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