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

2014/09/23 by Birgit Jacob, Jacob, Birgit, Kirsten Morris +3 · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA) #Numerical methods in inverse problems #Spectral Theory in Mathematical Physics #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1409.6524

openalex publication_date 2014/09/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Hyperbolic partial differential equations on a one-dimensional spatial domain\nare studied. This class of systems includes models of beams and waves as well\nas the transport equation and networks of non-homogeneous transmission lines.\nThe main result of this paper is a simple test for C₀-semigroup generation\nin terms of the boundary conditions. The result is illustrated with several\nexamples.\n

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