Abstract and Applied Analysis
Volume 2012 (2012), Article ID 531659, 20 pages
http://dx.doi.org/10.1155/2012/531659
Research Article

Exact Null Controllability of KdV-Burgers Equation with Memory Effect Systems

Rajagounder Ravi Kumar,1 Kil To Chong,2 and Jong Ho Park3

1CASY, DEIS, University of Bologna, Viale Risorgimento 2, 40136 Bologna, Italy
2Advanced Electronics and Information Research Center, Department of Electronics and Information Technology, Chonbuk National University, Republic of Korea
3Department of Electrical and Electronics Engineering, Seonam University, Republic of Korea

Received 12 August 2012; Accepted 7 November 2012

Academic Editor: Yongfu Su

Copyright © 2012 Rajagounder Ravi Kumar et al. 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 paper is concerned with exact null controllability analysis of nonlinear KdV-Burgers equation with memory. The proposed approach relies upon regression tool to prove controllability property of linearized KdV-Burgers equation via Carleman estimates. The control is distributed along with subdomain and the external control acts on the key role of observability inequality with memory. This description finally showed the exact null controllability guaranteeing the stability.