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arXiv · 1209.5564

Quantum graphs with mixed dynamics: the transport/diffusion case

Amru Hussein·Delio Mugnolo
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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.

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Amru Hussein, Delio Mugnolo. 2012-09-25. Quantum graphs with mixed dynamics: the transport/diffusion case. https://doi.org/10.1088/1751-8113/46/23/235202

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