Pseudo almost automorphic solutions of class \(r\) in \(\alpha\)-norm under the light of measure theory
type: Item
instance of: scholarly article
title: Pseudo almost automorphic solutions of class \(r\) in \(\alpha\)-norm under the light of measure theory
zbMATH Open document ID: 1471.34145
author: Issa Zabsonre
author: Djendode Mbainadji
published in: Nonautonomous Dynamical Systems
publication date: 2021-05-03T00:00:00Z
review text: The authors study the existence of pseudo almost automorphic solutions using the alpha-norm for some partial functional differential equations. The linear part is assumed to generate a compact analytic semigroup, the input function is almost automorphic. The authors assumed that the linear partial functional differential equation is hyperbolic. This assumption allows them to use a formula for bounded solutions and to prove the existence of pseudo almost automorphic solutions for the whole system. Some result are also given for nonlinear systems using the Banach fixed point theorem.
Mathematics Subject Classification ID: 34K30
Mathematics Subject Classification ID: 43A60
Mathematics Subject Classification ID: 34K14
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 44A35
Mathematics Subject Classification ID: 47D06
Mathematics Subject Classification ID: 47N20
zbMATH DE Number: 7342034
zbMATH Keywords: measure theory
zbMATH Keywords: ergodicity
zbMATH Keywords: \((\mu, v)\)-pseudo almost automorphic function
zbMATH Keywords: evolution equations
zbMATH Keywords: reaction diffusion system
zbMATH Keywords: partial functional differential equations
reviewed by: Khalil Ezzinbi
MaRDI profile type: Publication
full work available at URL: msds-2020-0112
OpenAlex ID: W3052127505
cites work: Reduction principle and dynamic behaviors for a class of partial functional differential equations
cites work: Q4810484
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cites work: Pseudo-Almost Periodic and Pseudo-Almost Automorphic Solutions to Some Evolution Equations Involving Theoretical Measure Theory
cites work: Pseudo almost automorphic solutions of class \(r\) for some partial functional differential equations
cites work: Cn-almost automorphic solutions for partial neutral functional differential equations
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cites work: Semigroups of linear operators and applications to partial differential equations
cites work: Existence, Stability, and Compactness in the α-Norm for Partial Functional Differential Equations
DOI: 10.1515/MSDS-2020-0112
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description: scientific article; zbMATH DE number 7342034