Premium
Diffusive stability for periodic metric graphs
Author(s) -
ChirilusBruckner Martina,
Maier Daniela,
Schneider Guido
Publication year - 2019
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201800125
Subject(s) - mathematics , real line , metric (unit) , graph , diffusion , mathematical analysis , stability (learning theory) , nonlinear system , discrete mathematics , combinatorics , physics , computer science , quantum mechanics , operations management , economics , machine learning
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 L 1 ‐ L ∞ estimates combined with Bloch wave analysis for periodic metric graphs.