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arXiv · 1409.6524

$C_0$-semigroups for hyperbolic partial differential equations on a one-dimensional spatial domain

Birgit Jacob·Kirsten Morris·Hans Zwart
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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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Birgit Jacob, Kirsten Morris, Hans Zwart. 2014-09-23. $C_0$-semigroups for hyperbolic partial differential equations on a one-dimensional spatial domain. https://arxiv.org/abs/1409.6524

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