``Buridan's ass'' problem in relaxation systems with one slow variable
type: Item
instance of: scholarly article
title: ``Buridan's ass'' problem in relaxation systems with one slow variable
zbMATH Open document ID: 0947.34042
DOI: 10.1007/BF02675018
author: A. Yu. Kolesov
author: N. Kh. Rozov
published in: Mathematical Notes
publication date: 2000-04-03T00:00:00Z
review text: Consider the singularly perturbed scalar differential equation \((*)\) \(\varepsilon dy/dx = f(x,y)\), \(0 < \varepsilon \ll 1\) where \(f\) is \(C^\infty\). It is assumed that \(f(x,y) =0\) has two solutions \(y = \varphi (x)\) and \(x = \psi (y)\) intersecting transversally at \((x_0 , y_0)\) and forming a pitchfork such that \(f^{-1} (0)\) has three branches for \(x > x_0\). The authors are interested in the asymptotic behavior of the solution \(y(x,\varepsilon)\) to \((*)\) satisfying \(y(x_0 - a, \varepsilon) = \alpha\) \((a > 0)\) as \(\varepsilon\) tends to zero, especially, they ask for the branch of \(f^{-1} (0)\) approximated by the solution \(y (x_0 - a,\varepsilon)\) for \(x> x_0\) and for conditions implying a delayed approximation. For proofs the authors refer to other papers.
Mathematics Subject Classification ID: 34D10
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 34E15
Mathematics Subject Classification ID: 34E05
Mathematics Subject Classification ID: 34D05
zbMATH DE Number: 1407543
zbMATH Keywords: exchange of stability
zbMATH Keywords: pitchfork bifurcation
zbMATH Keywords: delayed exchange of stability
Wikidata QID: Q59448693
reviewed by: Klaus R. Schneider
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/bf02675018
OpenAlex ID: W1975001336
description: scientific article; zbMATH DE number 1407543