Bi-Continuous semigroups for flows on infinite networks

Christian Budde; Marjeta Kramar Fijavž; Christian Budde; Marjeta Kramar Fijavž

doi:10.3934/nhm.2021017

Networks and Heterogeneous Media

2021, Volume 16, Issue 4: 553-567. doi: 10.3934/nhm.2021017

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Bi-Continuous semigroups for flows on infinite networks

Christian Budde ^{1
,},
Marjeta Kramar Fijavž ^{2
,
,}

1.
North-West University, School of Mathematical and Statistical Sciences, Private Bag X6001-209, Potchefstroom 2520, South Africa
2.
University of Ljubljana, Faculty of Civil and Geodetic Engineering, Jamova 2, SI-1000 Ljubljana, Slovenia, Institute of Mathematics, Physics and Mechanics, Jadranska 19, SI-1000 Ljubljana, Slovenia

Received: 01 December 2020 Revised: 01 May 2021 Published: 01 July 2021
Primary: 35R02; Secondary: 35F46, 47D06, 46A70

We study transport processes on infinite metric graphs with non-constant velocities and matrix boundary conditions in the $ {\mathrm{L}}^{\infty} $-setting. We apply the theory of bi-continuous operator semigroups to obtain well-posedness of the problem under different assumptions on the velocities and for general stochastic matrices appearing in the boundary conditions.
- Transport equations,
- infinite metric graphs,
- bi-continuous operator semigroups,
- Bochner $ {\mathrm{L}}^{\infty} $-spaces,
- perturbations
Citation: Christian Budde, Marjeta Kramar Fijavž. Bi-Continuous semigroups for flows on infinite networks[J]. Networks and Heterogeneous Media, 2021, 16(4): 553-567. doi: 10.3934/nhm.2021017

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Abstract

We study transport processes on infinite metric graphs with non-constant velocities and matrix boundary conditions in the $ {\mathrm{L}}^{\infty} $-setting. We apply the theory of bi-continuous operator semigroups to obtain well-posedness of the problem under different assumptions on the velocities and for general stochastic matrices appearing in the boundary conditions.

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