Finite propagation speed for solutions of the wave equation on metric graphs

2011/06/04 by Vadim Kostrykin, Kostrykin, Vadim, Jürgen Potthoff +3
Mathematics · Physics and Astronomy · #34B45 #35L05 #35L20 #Differential Equations and Boundary Problems #FOS: Physical sciences #Mathematical Physics (math-ph) #Spectral Theory in Mathematical Physics #advanced mathematical theories #math-ph #math.MP #msc:34B45 #msc:35L05 #msc:35L20

paper · pdf · doi:10.48550/arxiv.1106.0817

24 pages, 1 figure

arxiv created 2011/06/04 · openalex publication_date 2011/06/04 · arxiv updated 2011/06/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We provide a class of self-adjoint Laplace operators on metric graphs with the property that the solutions of the associated wave equation satisfy the finite propagation speed property. The proof uses energy methods, which are adaptions of corresponding methods for smooth manifolds.

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