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dc.contributor.authorBolikowski, Łukasz
dc.contributor.authorGokieli, Maria
dc.contributor.authorVarchon, Nicolas
dc.identifier.citationŁ. Bolikowski, M. Gokieli and N. Varchon, The Neumann problem in an irregular domain, Interfaces and Free Boundaries, Volume 12, Issue 4, 2010, pp. 443–462.en
dc.description.abstractWe consider the stability of patterns for the reaction-diffusion equation with Neumann boundary conditions in an irregular domain in ℝN, N ≥ 2, the model example being two convex regions connected by a small ‘hole’ in their boundaries. By patterns we mean solutions having an interface, i.e. a transition layer between two constants. It is well known that in 1D domains and in many 2D domains, patterns are unstable for this equation. We show that, unlike the 1D case, but as in 2D dumbbell domains, stable patterns exist. In a more general way, we prove invariance of stability properties for steady states when a sequence of domains Ωn converges to our limit domain in the sense of Mosco. We illustrate the theoretical results by numerical simulations of evolving and persisting interfaces.en
dc.publisherEMS, Interfaces and Free Boundariesen
dc.subjectsteady statesen
dc.subjectdomain variationen
dc.subjectMosco convergenceen
dc.titleThe Neumann problem in an irregular domainen
dc.contributor.organizationInterdyscyplinarne Centrum Modelowania Matematycznego i Komputerowego, Uniwersytet Warszawskipl_PL
dc.description.epersonMaria Gokieli

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