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

M. C. Leseduarte and R. Quintanilla

 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

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.