Mathematical Problems in Engineering
Volume 2009 (2009), Article ID 358329, 13 pages
doi:10.1155/2009/358329
Research Article

Well Posedness for a Class of Flexible Structure in Hölder Spaces

Claudio Cuevas1 and Carlos Lizama2

1Departamento de Matemática, Universidade Federal de Pernambuco, Av. Prof. Luiz Freire, S/N, Recife-PE, CEP. 50540-740, Brazil
2Departamento de Matemática, Facultad de Ciencias, Universidad de Santiago de Chile, Casilla 307-Correo 2, Santiago-Chile, Chile

Received 4 December 2008; Accepted 6 April 2009

Academic Editor: J. Rodellar

Copyright © 2009 Claudio Cuevas and Carlos Lizama. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We characterize well-posedness in Hölder spaces for an abstract version of the equation (∗) u′′+λu′′′=c2(Δu+μΔu′)+f which model the vibrations of flexible structures possessing internal material damping and external force f. As a consequence, we show that in case of the Laplacian with Dirichlet boundary conditions, equation (∗) is always well-posed provided 0<λ<μ.