Abstract and Applied Analysis
Volume 2011 (2011), Article ID 149091, 10 pages
http://dx.doi.org/10.1155/2011/149091
Research Article

Nonexistence Results for the Cauchy Problem for Nonlinear Ultraparabolic Equations

Sebti Kerbal1 and Mokhtar Kirane2

1Department of Mathematics and Statistics, Sultan Qaboos University, P.O. Box 36, Al-Khodh, Muscat 123, Oman
2Laboratoire de Mathématiques, Image et Applications, Pôle Sciences et Technologies, Université de La Rochelle, Avenue M. Crépeau, 17042 La Rochelle, France

Received 23 March 2011; Revised 21 May 2011; Accepted 14 June 2011

Academic Editor: Toka Diagana

Copyright © 2011 Sebti Kerbal and Mokhtar Kirane. 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

Nonexistence of global solutions to ultraparabolic equations and systems is presented. Our results fill a gap in the literature on ultraparabolic equations. The method of proof we use relies on a choice of a suitable test function in the weak formulation of the solutions of the problems under-study.