On spectral convergence for some parabolic problems with locally large diffusion
type: Item
instance of: scholarly article
title: On spectral convergence for some parabolic problems with locally large diffusion
zbMATH Open document ID: 1419.35105
DOI: 10.12775/TMNA.2018.025
author: Maria C. Carbinatto
author: Krzysztof P. Rybakowski
published in: Topological Methods in Nonlinear Analysis
publication date: 2019-05-07T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.tmna/1541473240
review text: The authors study the abstract parabolic problem \[ \dot u=-A_{\varepsilon}u+f_{\varepsilon}(u),\tag{1} \] on $H^1(0,1)$, and a corresponding limit problem \[ \dot z=-A_0z+f_0(z),\tag{2} \] on $\mathbb{R}^n$, where $(A_{\varepsilon})_{\varepsilon\in (0,\varepsilon_0)}$, ($\varepsilon_0\in (0,\infty)$), is a family of linear operators which satisfy some assumptions on a strictly increasing sequence $(x_j)_{j\in [0..n]}$ in $[0,1]$, $A_0$ is the limit operator for $\varepsilon\to 0$, and $f_{\varepsilon}$ and $f_0$, $\varepsilon\in (0,\varepsilon_0)$, are Nemitski operators generated by nonlinearities satisfying an appropriate condition. They prove a spectral convergence result and some Conley index continuation principles for the families of local semiflows generated by problems $(1)$ and $(2)$.
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 37B30
Mathematics Subject Classification ID: 35B25
zbMATH DE Number: 7051684
zbMATH Keywords: spectra convergence
zbMATH Keywords: localized large diffusion
zbMATH Keywords: singular perturbations
zbMATH Keywords: Conley index
reviewed by: Rodica Luca
MaRDI profile type: Publication
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OpenAlex ID: W2900037743
Wikidata QID: Q128983607
description: scientific article; zbMATH DE number 7051684