Strong periodic solutions for a class of abstract evolution equations.
type: Item
instance of: scholarly article
title: Strong periodic solutions for a class of abstract evolution equations.
zbMATH Open document ID: 1037.34049
DOI: 10.1016/S0362-546X(03)00125-1
author: Grzegorz Łukaszewicz
author: Elva E. Ortega-Torres
author: Rojas-Medar Marko Antonio
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2003-08-13T00:00:00Z
review text: The authors deal with the existence, uniqueness and stability of strong periodic solutions to a class of abstract evolution equations of the form \[ \frac d{dt}u + Lu + B(u,u)+ Ru = f \] in a separable Hilbert space \(H\). Here, \(L\) is a selfadjoint strictly positive operator on \(H\), \(B\) a bilinear form on \(H\times H\), \(R\) a linear operator and \(f\) a periodic function. The main tool for proving the results is based on some estimates on approximation solutions. An application of the existence theorem to the system of equations of magneto-micropolar fluids and the Navier-Stokes system is given, too.
Mathematics Subject Classification ID: 34G20
Mathematics Subject Classification ID: 35Q35
Mathematics Subject Classification ID: 35B10
zbMATH DE Number: 1963678
zbMATH Keywords: strong periodic solutions
zbMATH Keywords: existence
zbMATH Keywords: uniqueness
zbMATH Keywords: stability
zbMATH Keywords: Galerkin approximation
zbMATH Keywords: Navier-Stokes equation
zbMATH Keywords: fluids
reviewed by: Józef Myjak
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1963678