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c 0-semigroup

ESAIM: Control, Optimisation and Calculus of Variations (1)

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Well-posedness and regularity of hyperbolic boundary control systemson a one-dimensional spatial domain
Hans Zwart, Yann Le Gorrec, Bernhard Maschke, Javier Villegas
Journal:

ESAIM: Control, Optimisation and Calculus of Variations / Volume 16 / Issue 4 / October 2010

Published online by Cambridge University Press:

25 August 2009, pp. 1077-1093

Print publication:

October 2010
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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 C 0-semigroup. Furthermore, we show that the corresponding transfer function is regular, i.e., has a limit for s going to infinity.