Stabilization of the wave equation on 1-D networks

Valein J, Zuazua E (2009)

Publication Type: Journal article

Publication year: 2009

Journal

SIAM Journal on Control and Optimization Society for Industrial and Applied Mathematics

Book Volume: 48

Pages Range: 2771-2797

Journal Issue: 4

DOI: 10.1137/080733590

Abstract

In this paper we study the stabilization of the wa ve equation on general 1-d networks. For that, we transfer known observability results in the context of control problems of conservative systems (see [R. Dáger and E. Zuazua, Wave Propagation, Observation, and Control in 1-d Flexible Multi-structures, Math. Appl. 50, Springer-Verlag, Berlin, 2006]) into a weighted observability estimate for dissipative systems. Then we use an interpolation inequality similar to the one proved in [P. Bégout and F. Soria, J. Differential Equations, 240 (2007), pp. 324-356] to obtain the explicit decay estimates of the energy for smooth initial data. The obtained decay rate depends on the geometric and topological properties of the network. We also give some examples of particular networks in which our results apply, yielding different decay rates.

Authors with CRIS profile

Enrique Zuazua Iriondo

Involved external institutions

Université polytechnique des Hauts-de-France (UPHF, UVHC) FR France (FR) Basque Center of Applied Mathematics (BCAM) ES Spain (ES)

How to cite

APA:

Valein, J., & Zuazua, E. (2009). Stabilization of the wave equation on 1-D networks. SIAM Journal on Control and Optimization, 48(4), 2771-2797. https://dx.doi.org/10.1137/080733590

MLA:

Valein, Julie, and Enrique Zuazua. "Stabilization of the wave equation on 1-D networks." SIAM Journal on Control and Optimization 48.4 (2009): 2771-2797.

BibTeX: Download