Differential Equations and Nonlinear Mechanics
Volume 2006 (2006), Article ID 68748, 14 pages
doi:10.1155/DENM/2006/68748
Instability, nonexistence, and uniqueness in elasticity with porous dissipation
Departament de Matemàtica Aplicada 2, Universitat Politècnica de Catalunya, Colom 11, Terrassa, Barcelona 08222, Spain
Received 18 July 2005; Revised 10 October 2005; Accepted 11 October 2005
Copyright © 2006 M. C. Leseduarte and R. Quintanilla. 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
This paper is devoted to the study of the elasticity with porous
dissipation. In the context of the nonlinear problem, we prove
instability and nonexistence of solutions. In the context of the
linear problem, we obtain exponential growth. We also obtain
uniqueness of solutions of the backward in time problem of the
linear equations.