Multiple tunnel effect for dispersive waves on a star-shaped network: an explicit formula for the spectral representation

DOI10.1007/s00028-012-0143-5zbMath1257.35121arXiv1012.3068OpenAlexW2005639914MaRDI QIDQ692805

Robert Haller-Dintelmann, Felix Ali Mehmeti, Virginie Régnier

Publication date: 6 December 2012

Published in: Journal of Evolution Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1012.3068

zbMATH Keywords

Klein-Gordon equationevolution equationsfunctional calculusgeneralized eigenfunctionsdynamics of the tunnel effectgeneralized Fourier-type inversion formula

Mathematics Subject Classification ID

Transform methods (e.g., integral transforms) applied to PDEs (35A22) Functional calculus for linear operators (47A60) Spectrum, resolvent (47A10) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42A38) (Generalized) eigenfunction expansions of linear operators; rigged Hilbert spaces (47A70) Second-order semilinear hyperbolic equations (35L71) Initial-boundary value problems for second-order hyperbolic systems (35L53)

Related Items

The deformations problem for the Stieltjes strings system with a nonlinear condition ⋮ Dispersive effects for the Schrödinger equation on the tadpole graph ⋮ Energy Flow Above the Threshold of Tunnel Effect ⋮ Singularly perturbed hyperbolic problems on metric graphs: asymptotics of solutions ⋮ The Influence of the Tunnel Effect on L ∞-time Decay

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