Journal of Applied Mathematics
Volume 2004 (2004), Issue 3, Pages 201-211

Blowup of solutions with positive energy in nonlinear thermoelasticity with second sound

Salim A. Messaoudi1 and Belkacem Said-Houari2

1Mathematical Sciences Department, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia
2Département de Mathématiques, Université Badji Mokhtar, BP 12, Annaba 23000, Algeria

Received 6 November 2003; Revised 14 April 2004

Copyright © 2004 Salim A. Messaoudi and Belkacem Said-Houari. 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.


This work is concerned with a semilinear thermoelastic system, where the heat flux is given by Cattaneo's law instead of the usual Fourier's law. We will improve our earlier result by showing that the blowup can be obtained for solutions with “relatively” positive initial energy. Our technique of proof is based on a method used by Vitillaro with the necessary modifications imposed by the nature of our problem.