Telegraph systems on networks and port-Hamiltonians. Ⅲ. Explicit representation and long-term behaviour-Reference-Cited by-同舟云学术

Telegraph systems on networks and port-Hamiltonians. Ⅲ. Explicit representation and long-term behaviour

Published:2022 Issue:6 Volume:11 Page:2165
ISSN:2163-2480
Container-title:Evolution Equations and Control Theory
language:
Short-container-title:EECT

Author:

Banasiak Jacek¹²,Błoch Adam²

Affiliation:

1. Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria, South Africa

2. Institute of Mathematics, Łodź University of Technology, Łodź, Poland

Abstract

<p style='text-indent:20px;'>In this paper we present an explicit formula for the semigroup governing the solution to hyperbolic systems on a metric graph, satisfying general linear Kirchhoff's type boundary conditions. Further, we use this representation to establish the long term behaviour of the solutions. The crucial role is played by the spectral decomposition of the boundary matrix.</p>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

Applied Mathematics,Control and Optimization,Modeling and Simulation

Reference24 articles.

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2. J. Banasiak.Explicit formulae for limit periodic flows on networks, Linear Algebra and its Applications, 500 (2016), 30-42.

3. J. Banasiak and A. Błoch, Telegraph systems on networks and port-Hamiltonians. I. Boundary conditions and well-posedness, Evol. Eq. Control Th., (2021).

4. J. Banasiak, A. Błoch.Telegraph systems on networks and port-Hamiltonians. Ⅱ. Network realizability, Netw. Heterog. Media, 17 (2022), 73-99.

5. J. Banasiak, A. Falkiewicz, P. Namayanja.Semigroup approach to diffusion and transport problems on networks, Semigroup Forum, 93 (2016), 427-443.