Journal of Applied Mathematics
Volume 2004 (2004), Issue 3, Pages 201-211
doi:10.1155/S1110757X04311022
Blowup of solutions with positive energy in nonlinear
thermoelasticity with second sound
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.
Abstract
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.