6533b82ffe1ef96bd1295b91

RESEARCH PRODUCT

Quantum graphs with mixed dynamics: the transport/diffusion case

Amru HusseinDelio Mugnolo

subject

Statistics and ProbabilityPhysicsPartial differential equationSemigroupMathematical analysis34B45 47D06 47N50Hilbert spaceFOS: Physical sciencesGeneral Physics and AstronomyBoundary (topology)Statistical and Nonlinear PhysicsMathematical Physics (math-ph)System of linear equationssymbols.namesakeMathematics - Analysis of PDEsModeling and SimulationQuantum graphFOS: MathematicssymbolsDiffusion (business)Transport phenomenaMathematical PhysicsAnalysis of PDEs (math.AP)

description

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.

yearjournalcountryeditionlanguage
2013-05-21
10.1088/1751-8113/46/23/235202http://arxiv.org/abs/1209.5564