Quasilinear abstract parabolic evolution equations and exponential attractors
type: Item
instance of: scholarly article
title: Quasilinear abstract parabolic evolution equations and exponential attractors
zbMATH Open document ID: 1073.37090
author: Masashi Aida
author: Messoud Efendiev
author: Atsushi Yagi
published in: Osaka Journal of Mathematics
publication date: 2005-05-06T00:00:00Z
review text: The authors suggest a general strategy for construction of an exponential attractor for a dynamical system determined from the quasilinear abstract parabolic evolution equation \(\frac{dU}{dt}=A(U)U=F(U)\), \(0<t<\infty\), \(U(0)=U_0\), in a Banach space \(X\). Here, \(Z\) is a Banach space continuously imbedded in \(X\), \(K\) is an open ball in \(Z\) and for each \(U\in K\) \(A(U)\) is a densely defined closed linear operator in \(X\) with the domain \(D(A(U))\) independent of \(U\in K\); \(F\) is a nonlinear operator from \(K\) into \(X\). The obtained abstract results are applied to the chemotaxis-growth system in nonsmooth domain.
Mathematics Subject Classification ID: 37L30
Mathematics Subject Classification ID: 35B41
Mathematics Subject Classification ID: 35K90
Mathematics Subject Classification ID: 92C17
zbMATH DE Number: 2165815
zbMATH Keywords: abstract parabolic evolution equation
zbMATH Keywords: dynamical system
zbMATH Keywords: exponential attractor
zbMATH Keywords: chemotaxis-growth system
reviewed by: Boris V. Loginov
MaRDI profile type: Publication
Recommended article: Exponential attractors for a quasilinear parabolic equation
Recommended article: Q4407532
Recommended article: Q3372906
Recommended article: Quasilinear Evolution Equations and Parabolic Systems
Recommended article: Abstract quasilinear parabolic equations
Recommended article: Dynamic theory of quasilinear parabolic equations—I. Abstract evolution equations
Recommended article: Attractors of asymptotically autonomous quasi-linear parabolic equation with spatially variable exponents
Recommended article: Q5455514
Recommended article: Q4713492
Recommended article: Q5688762
description: scientific article; zbMATH DE number 2165815