Perturbation quasi différentielle d'un semi-groupe régularisant dans une échelle d'espaces de Banach. (Quasi differential perturbation of a regularizing semigrop in a scale of Banach spaces)
type: Item
instance of: scholarly article
title: Perturbation quasi différentielle d'un semi-groupe régularisant dans une échelle d'espaces de Banach. (Quasi differential perturbation of a regularizing semigrop in a scale of Banach spaces)
zbMATH Open document ID: 0654.47020
DOI: 10.1016/S0294-1449(16)30365-1
author: Jean Duchon
author: Raoul Robert
published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire
publication date: 1987-01-01T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/78137
review text: The authors give a global existence and uniqueness result for the evolution equation \(u_ t+Au=F(u)\), \(u(0)=u_ 0\), where -A is the infinitesimal generator of a linear semigroup S(t) smoothing in a scale of Banach spaces \(B_{\rho}\) \((0\leq \rho <\infty)\) and F is a nonlinear quasi differential operator consistent with S(t). They show that for \(u_ 0\) small enough in \(B_ 0\) there is a unique solution of the equation such that u(t) remains bounded in \(B_{\alpha t}\), for some \(\alpha >0\). The authors apply this result to the motion of the interface of two liquids in porous medium.
Mathematics Subject Classification ID: 47D03
Mathematics Subject Classification ID: 35R20
Mathematics Subject Classification ID: 47H20
zbMATH DE Number: 4067669
zbMATH Keywords: perturbations
zbMATH Keywords: global existence and uniqueness result
zbMATH Keywords: evolution equation
zbMATH Keywords: scale of Banach spaces
zbMATH Keywords: nonlinear quasi differential operator
zbMATH Keywords: motion of the interface of two liquids in porous medium
reviewed by: Marek Cezary Zdun
MaRDI profile type: Publication
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OpenAlex ID: W2280911355
description: scientific article; zbMATH DE number 4067669