Author:
Budde Christian,Fijavž Marjeta Kramar
Abstract
<p style='text-indent:20px;'>We study transport processes on infinite metric graphs with non-constant velocities and matrix boundary conditions in the <inline-formula><tex-math id="M1">\begin{document}$ {\mathrm{L}}^{\infty} $\end{document}</tex-math></inline-formula>-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.</p>
Publisher
American Institute of Mathematical Sciences (AIMS)
Subject
Applied Mathematics,Computer Science Applications,General Engineering,Statistics and Probability,Applied Mathematics,Computer Science Applications,General Engineering,Statistics and Probability
Reference32 articles.
1. A. Albanese, F. Kühnemund.Trotter-Kato approximation theorems for locally equicontinuous semigroups, Riv. Mat. Univ. Parma (7), 1 (2002), 19-53.
2. A. A. Albanese, L. Lorenzi, V. Manco.Mean ergodic theorems for bi-continuous semigroups, Semigroup Forum, 82 (2011), 141-171.
3. A. A. Albanese, E. Mangino.Trotter-Kato theorems for bi-continuous semigroups and applications to Feller semigroups, Journal of Mathematical Analysis and Applications, 289 (2004), 477-492.
4. W. Arendt, A. Grabosch, G. Greiner, U. Groh, H. P. Lotz, U. Moustakas, R. Nagel, F. Neubrander and U. Schlotterbeck, One-Parameter Semigroups of Positive Operators, vol. 1184 of Lecture Notes in Mathematics, Springer-Verlag, Berlin, 1986.
5. J. Banasiak, A. Falkiewicz.Some transport and diffusion processes on networks and their graph realizability, Appl. Math. Lett., 45 (2015), 25-30.
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