A strange vertex condition coming from nowhere

Rösler, Frank 2021. A strange vertex condition coming from nowhere. SIAM Journal on Mathematical Analysis 53 (3) , pp. 3098-3122. 10.1137/20M1322194

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Abstract

We prove norm-resolvent and spectral convergence of solutions to the Neumann-Poisson problem on a domain perforated by Dirichlet-holes and shrinking to a 1-dimensional interval. The limit satisfies an equation of the type -u'' + cu = f on the interval, where c is a positive constant. As an application we study the convergence of solutions in perforated graph-like domains. We show that if the scaling between the edge neighbourhood and the vertex neighbourhood is chosen correctly, the constant c will appear in the vertex condition of the limit problem. In particular, this implies that the spectrum of the resulting quantum graph is altered in a controlled way by the perforation.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Publisher:	Society for Industrial and Applied Mathematics
ISSN:	0036-1410
Date of First Compliant Deposit:	5 May 2021
Date of Acceptance:	10 February 2021
Last Modified:	15 Nov 2023 23:26
URI:	https://orca.cardiff.ac.uk/id/eprint/138481

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