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Title: Existence, local uniqueness and asymptotic approximation of spike solutions to singularly perturbed elliptic problems
Authors: Omel'chenko, OlehRecke, Lutz
Issue Date: 2011
Published in: Preprint / Weierstraß-Institut für Angewandte Analysis und Stochastik, Volume 1607, ISSN 0946-8633
Publisher: Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik
Abstract: This paper concerns general singularly perturbed second order semilinear elliptic equations on bounded domains $Omega subset R^n$ with nonlinear natural boundary conditions. The equations are not necessarily of variational type. We describe an algorithm to construct sequences of approximate spike solutions, we prove existence and local uniqueness of exact spike solutions close to the approximate ones (using an Implicit Function Theorem type result), and we estimate the distance between the approximate and the exact solutions. Here ''spike solution'' means that there exists a point in $Omega$ such that the solution has a spike-like shape in a vicinity of such point and that the solution is approximately zero away from this point. The spike shape is not radially symmetric in general and may change sign.
Keywords: Non-variational problem; Interior spike; Boundary layer; Implicit function theorem
DDC: 510
License: This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.
Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.
Appears in Collections:Mathematik

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