Volume 16, Number 4, October-December 2010
|Page(s)||1077 - 1093|
|Published online||25 August 2009|
Well-posedness and regularity of hyperbolic boundary control systems on a one-dimensional spatial domain
Department of Applied Mathematics, University of Twente,
7500 AE Enschede, The Netherlands. firstname.lastname@example.org
2 FEMTO-ST AS2M, 24 rue Alain Savary, 25000 Besançon, France. Yann.Le.Gorrec@ens2m.fr
3 LAGEP, CNRS UMR 5007, CPE Lyon – Bâtiment 308 G, Université Lyon-1, Université de Lyon, 43 bd. du 11 Novembre 1918, 69622 Villeurbanne Cedex, France. email@example.com
4 AVL Powertrain UK, Langdale House, Sable Way, Southfields Business Park, Basildon, SS15 6SR, UK. Javier.Villegas@avl.com
Revised: 1 April 2009
We study a class of hyperbolic partial differential equations on a one dimensional spatial domain with control and observation at the boundary. Using the idea of feedback we show these systems are well-posed in the sense of Weiss and Salamon if and only if the state operator generates a C0-semigroup. Furthermore, we show that the corresponding transfer function is regular, i.e., has a limit for s going to infinity.
Mathematics Subject Classification: 93C20 / 35L40 / 35F15 / 37Kxx
Key words: Infinite-dimensional systems / hyperbolic boundary control systems / C0-semigroup / well-posedness / regularity
© EDP Sciences, SMAI, 2009
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