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arXiv · 1712.03030

Waves and Diffusion on Metric Graphs with General Vertex Conditions

Klaus-Jochen Engel·Marjeta Kramar Fijavž
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Abstract

We prove well-posedness for very general linear wave- and diffusion equations on compact or non-compact metric graphs allowing various different conditions in the vertices. More precisely, using the theory of strongly continuous operator semigroups we show that a large class of (not necessarily self-adjoint) second order differential operators with general (possibly non-local) boundary conditions generate cosine families, hence also analytic semigroups, on ${\mathrm{L}}^p({\mathbb{R}_+},{\mathbb{C}}^{\ell})\times{\mathrm{L}}^p([0,1],{\mathbb{C}}^m)$ for $1\le p<+\infty$.

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Klaus-Jochen Engel, Marjeta Kramar Fijavž. 2017-12-08. Waves and Diffusion on Metric Graphs with General Vertex Conditions. https://doi.org/10.3934/eect.2019030

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