C0-semigroups for hyperbolic partial differential equations on a one-dimensional spatial domain

Birgit Jacob; Kirsten Morris; Hans Zwart

doi:10.1007/s00028-014-0271-1

C₀-semigroups for hyperbolic partial differential equations on a one-dimensional spatial domain

Birgit Jacob^*, Kirsten Morris, Hans Zwart

^*Corresponding author for this work

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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 nonhomogeneous 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.

Original language	English
Pages (from-to)	493-502
Number of pages	10
Journal	Journal of evolution equations
Volume	15
Issue number	2
DOIs	https://doi.org/10.1007/s00028-014-0271-1
Publication status	Published - Jun 2015

Keywords

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10.1007/s00028-014-0271-1

ArticleFinal published version, 427 KBLicence: Taverne

Cite this

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title = "C0-semigroups for hyperbolic partial differential equations on a one-dimensional spatial domain",

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 nonhomogeneous 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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AB - 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 nonhomogeneous 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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