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      Bi-continuous semigroups for flows in infinite networks

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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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          Most cited references 17

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          Spectral properties and asymptotic periodicity of flows in networks

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            A Hille-Yosida theorem for Bi-continuous semigroups

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              The eigenvalues of the Laplacian on locally finite networks

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                Author and article information

                Journal
                29 January 2019
                Article
                1901.10292

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

                Custom metadata
                35R02, 35F46, 47D06, 46A70
                12 pages
                math.AP math.FA

                Analysis, Functional analysis

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