Quantum graphs with mixed dynamics: the transport/diffusion case

Abstract

We introduce a class of partial differential equations on metric graphs associated with mixed evolution: on some edges we consider diffusion processes, on other ones transport phenomena. This yields a system of equations with possibly nonlocal couplings at the boundary. We provide sufficient conditions for these to be governed by a contractive semigroup on a Hilbert space naturally associated with the system. We show that our setting is also adequate to discuss specific systems of diffusion equations with boundary delays.

16 pages

References in corpus (1)

• Periodic Orbit Theory and Spectral Statistics for Quantum Graphs

Cited by in corpus (4)

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• Linear Hyperbolic Systems on Networks
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