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C 0-semigroups for hyperbolic partial differential equations on a one-dimensional spatial domain

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Abstract

Hyperbolic partial differential equations on a one-dimensional spatial domain are studied. This class of systems includes models of beams and waves as well as the transport equation and networks of non-homogeneous transmission lines. The main result of this paper is a simple test for C 0-semigroup generation in terms of the boundary conditions. The result is illustrated with several examples.

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Authors and Affiliations

  1. Fachbereich C - Mathematik und Naturwissenschaften, Arbeitsgruppe Funktionalanalysis University of Wuppertal, Gaußstraße 20, 42119, Wuppertal, Germany

    Birgit Jacob

  2. Department of Applied Mathematics, University of Waterloo, Waterloo, ON, N2L 3G1, Canada

    Kirsten Morris

  3. Department of Applied Mathematics, Faculty of Electrical Engineering, Mathematics and Computer Science, University of Twente, P.O. Box 217, 7500, AE, Enschede, The Netherlands

    Hans Zwart

Authors
  1. Birgit Jacob
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  2. Kirsten Morris
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  3. Hans Zwart
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Correspondence to Birgit Jacob.

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Jacob, B., Morris, K. & Zwart, H. C 0-semigroups for hyperbolic partial differential equations on a one-dimensional spatial domain. J. Evol. Equ. 15, 493–502 (2015). https://doi.org/10.1007/s00028-014-0271-1

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  • DOI: https://doi.org/10.1007/s00028-014-0271-1

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