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arXiv · 2110.08553

Flows on Metric Graphs with General Boundary Conditions

Klaus-Jochen Engel·Marjeta Kramar Fijavž
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Abstract

In this note we study the generation of $C_0$-semigroups by first order differential operators on $\mathrm{L}^p (\mathbb{R}_+,\mathbb{C}^{\ell})\times \mathrm{L}^p ([0,1],\mathbb{C}^{m})$ with general boundary conditions. In many cases we are able to characterize the generation property in terms of the invertibility of a matrix associated to the boundary conditions. The abstract results are used to study well-posedness of transport equations on non-compact metric graphs.

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Klaus-Jochen Engel, Marjeta Kramar Fijavž. 2021-10-16. Flows on Metric Graphs with General Boundary Conditions. https://arxiv.org/abs/2110.08553

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