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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.

### Most cited references17

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### Spectral properties and asymptotic periodicity of flows in networks

(2005)
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### A Hille-Yosida theorem for Bi-continuous semigroups

(2003)
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• Record: found

### The eigenvalues of the Laplacian on locally finite networks

(2005)
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### Author and article information

###### Journal
29 January 2019
###### Article
1901.10292