Diffusive stability for periodic metric graphs

Martina Chirilus‐Bruckner, Daniela Maier and Guido Schneider

Mathematische Nachrichten, 2019, vol. 292, issue 6, 1246-1259

Abstract: We consider a nonlinear diffusion equation on an infinite periodic metric graph. We prove that the terms which are irrelevant w.r.t. linear diffusion on the real line are irrelevant w.r.t. linear diffusion on the periodic metric graph, too. The proof is based on L1‐L∞ estimates combined with Bloch wave analysis for periodic metric graphs.

Date: 2019
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https://doi.org/10.1002/mana.201800125

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