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

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

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.