Eigenfunction Expansion Method for a Damped Boussinesq Equation
by
Andras Balogh
Department of Mathematics, The University of Texas - Pan American
Coauthors: Vladimir Varlamov (Department of Mathematics, The University of Texas - Pan American)

A damped Boussinesq equation representing an elastic membrane is considered on a disk with an external force acting as a distributed control. The eigenfunction expansion method enables us to explicitly construct solutions for the case of small initial data. Although it is used mainly as a theoretical tool, in this talk we demonstrate that the eigenfunction expansion method is effective in numerical simulations as well. We consider nonlinear terms of the power type and investigate solutions numerically. After demonstrating the theoretical convergence properties of the expansion we obtain explicit bounds on the size of the initial data that is required for the convergence of the series. We also examine the long-time asymptotics of solutions.

Date received: February 21, 2004

Copyright © 2004 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cakt-58.