Waves and diffusion on metric graphs with general vertex conditions

DOI10.3934/eect.2019030OpenAlexW2775383814WikidataQ127802383 ScholiaQ127802383MaRDI QIDQ2327330

Marjeta Kramar Fijavž, Klaus-Jochen Engel

Publication date: 14 October 2019

Published in: Evolution Equations and Control Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1712.03030

zbMATH Keywords

analytic semigroupssecond order differential operatorscosine familiesgeneral boundary conditionsmetric graphswaves and diffusion on networks

Mathematics Subject Classification ID

One-parameter semigroups and linear evolution equations (47D06) Heat equation (35K05) Wave equation (35L05) PDEs on graphs and networks (ramified or polygonal spaces) (35R02) Initial-boundary value problems for systems of linear higher-order PDEs (35G46)

Related Items (12)

Well-posedness and exponential stability of boundary control systems with dynamic boundary conditions ⋮ Flows on metric graphs with general boundary conditions ⋮ Telegraph systems on networks and port-Hamiltonians. I. Boundary conditions and well-posedness ⋮ Asymptotic behaviour for local and nonlocal evolution equations on metric graphs with some edges of infinite length ⋮ Well-posedness of systems of 1-D hyperbolic partial differential equations ⋮ On the parabolic Cauchy problem for quantum graphs with vertex noise ⋮ Concatenation of Nonhonest Feller Processes, Exit Laws, and Limit Theorems on Graphs ⋮ Laplacians with Point Interactions—Expected and Unexpected Spectral Properties ⋮ Asymptotic behaviour of fast diffusions on graphs ⋮ Stochastic reaction-diffusion equations on networks ⋮ Telegraph systems on networks and port-Hamiltonians. III: Explicit representation and long-term behaviour ⋮ Hidden symmetries in non-self-adjoint graphs

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