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

Authors

Birgit Jacob, Kirsten Morris, Hans Zwart

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.

Keywords

\( C_0 \)-semigroups; Hyperbolic partial differential equations; Port-Hamiltonian differential equations

Citation

• Journal: Journal of Evolution Equations
• Year: 2015
• Volume: 15
• Issue: 2
• Pages: 493–502
• Publisher: Springer Science and Business Media LLC
• DOI: 10.1007/s00028-014-0271-1

BibTeX

@article{Jacob_2015,
  title={{C 0-semigroups for hyperbolic partial differential equations on a one-dimensional spatial domain}},
  volume={15},
  ISSN={1424-3202},
  DOI={10.1007/s00028-014-0271-1},
  number={2},
  journal={Journal of Evolution Equations},
  publisher={Springer Science and Business Media LLC},
  author={Jacob, Birgit and Morris, Kirsten and Zwart, Hans},
  year={2015},
  pages={493--502}
}

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References

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