- About this Journal
- Abstracting and Indexing
- Aims and Scope
- Annual Issues
- Article Processing Charges
- Articles in Press
- Author Guidelines
- Bibliographic Information
- Citations to this Journal
- Contact Information
- Editorial Board
- Editorial Workflow
- Free eTOC Alerts
- Publication Ethics
- Reviewers Acknowledgment
- Submit a Manuscript
- Subscription Information
- Table of Contents
Abstract and Applied Analysis
Volume 2012 (2012), Article ID 156541, 12 pages
On the Regularized Solutions of Optimal Control Problem in a Hyperbolic System
Department of Mathematics, Faculty of Science, Atatürk University, 25240 Erzurum, Turkey
Received 7 March 2012; Accepted 12 June 2012
Academic Editor: Valery Covachev
Copyright © 2012 Yeşim Saraç and Murat Subaşı. 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.
- J.-L. Lions, Optimal Control of Systems Governed by Partial Differential Equations, Translated from the French by S. K. Mitter. Die Grundlehren der mathematischen Wissenschaften, Band 170, Springer, New York, NY, USA, 1971.
- M. Negreanu and E. Zuazua, “Uniform boundary controllability of a discrete 1-D wave equation,” Systems & Control Letters, vol. 48, no. 3-4, pp. 261–279, 2003.
- L. I. Bloshanskaya and I. N. Smirnov, “Optimal boundary control by an elastic force at one end and a displacement at the other end for an arbitrary sufficiently large time interval in the string vibration problem,” Differential Equations, vol. 45, no. 6, pp. 878–888, 2009.
- A. Smyshlyaev and M. Krstic, “Boundary control of an anti-stable wave equation with anti-damping on the uncontrolled boundary,” Systems & Control Letters, vol. 58, no. 8, pp. 617–623, 2009.
- X. Feng, S. Lenhart, V. Protopopescu, L. Rachele, and B. Sutton, “Identification problem for the wave equation with Neumann data input and Dirichlet data observations,” Nonlinear Analysis, vol. 52, no. 7, pp. 1777–1795, 2003.
- A. Münch, P. Pedregal, and F. Periago, “Optimal design of the damping set for the stabilization of the wave equation,” Journal of Differential Equations, vol. 231, no. 1, pp. 331–358, 2006.
- J. D. Benamou, “Domain decomposition, optimal control of systems governed by partial differential equations, and synthesis of feedback laws,” Journal of Optimization Theory and Applications, vol. 102, no. 1, pp. 15–36, 1999.
- F. Periago, “Optimal shape and position of the support for the internal exact control of a string,” Systems & Control Letters, vol. 58, no. 2, pp. 136–140, 2009.
- O. A. Ladyzhenskaya, Boundary Value Problems of Mathematical Physics, vol. 49 of Applied Mathematical Sciences, Springer, New York, NY, USA, 1985.
- E. Zeidler, Nonlinear Functional Analysis and Its Applications. III: Variational Methods and Optimization, Springer, New York, NY, USA, 1985.