Semigroups for dynamical processes on metric graphs

Abstract

We present the operator semigroups approach to first- and second-order dynamical systems taking place on metric graphs. We briefly survey the existing results and focus on the well-posedness of the problems with standard vertex conditions. Finally, we show two applications to biological models.

To be published in Phil. Trans. R. Soc. A 378: 20190619

References in corpus (8)

• Kirchhoff's Rule for Quantum Wires
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• Exact and Positive Controllability of Boundary Control Systems
• Diffusion in networks with time-dependent transmission conditions
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Cited by in corpus (3)

• Linear Hyperbolic Systems on Networks
• On the parabolic Cauchy problem for quantum graphs with vertex noise
• Well-posedness of non-autonomous transport equation on metric graphs