Locally Lipschitz perturbations of bisemigroups
type: Item
instance of: scholarly article
title: Locally Lipschitz perturbations of bisemigroups
zbMATH Open document ID: 1191.47080
author: Mohamed Sami ElBialy
published in: Communications on Pure and Applied Analysis
publication date: 2010-05-25T00:00:00Z
review text: This paper studies a class of ill-posed semilinear systems in abstract Banach spaces. The main result establishes the existence and uniqueness of local dichotomous mild solutions for any sufficiently small time interval \([t_1,t_2]\). Moreover, it is shown that the uniform \(C^0\)-norm of local dichotomous mild solutions depends continuously on \([t_1, t_2]\). It is also provided a simple example of a semilinear elliptic system that arises when considering solitary waves in an infinite cylinder. The proofs rely on standard arguments in the theory of nonlinear equations with infinitesimal generators in Banach spaces.
reviewed by: Vicenţiu D. Rădulescu
Mathematics Subject Classification ID: 47J06
Mathematics Subject Classification ID: 47D06
Mathematics Subject Classification ID: 34D09
Mathematics Subject Classification ID: 74J35
Mathematics Subject Classification ID: 34G20
Mathematics Subject Classification ID: 35J91
Mathematics Subject Classification ID: 35R25
zbMATH DE Number: 5711079
zbMATH Keywords: bi-semigroups
zbMATH Keywords: solitary waves
zbMATH Keywords: modulated waves
zbMATH Keywords: elliptic equations
zbMATH Keywords: exponential dichotomies
zbMATH Keywords: evolution equations
zbMATH Keywords: block operators
zbMATH Keywords: semigroup perturbations
zbMATH Keywords: Riccati equations
zbMATH Keywords: ill-posed problems
MaRDI profile type: Publication
full work available at URL: cpaa.2010.9.327
OpenAlex ID: W2073467450
DOI: 10.3934/CPAA.2010.9.327
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description: scientific article; zbMATH DE number 5711079