Parabolic evolution equations in interpolation and extrapolation spaces
type: Item
instance of: scholarly article
title: Parabolic evolution equations in interpolation and extrapolation spaces
zbMATH Open document ID: 0654.47019
DOI: 10.1016/0022-1236(88)90120-6
author: Herbert Amann
published in: Journal of Functional Analysis
publication date: 1988-01-01T00:00:00Z
review text: This paper deals with the Cauchy problem \(\dot u+A(t)u=f(t)\) in a Banach space \(X_ 0\), where A is a linear operator with time variable domain D(A(t)). In the first part it is assumed the existence of Banach spaces \(X_ 1\) and \(X_{\nu}\) such that \(D(A(t))=X_ 1\subset X_{\nu}\subset X_ 0\) and A has some properties related to \(X_{\nu}\). One proves the existence for the Cauchy problem associated with \(A_{\nu}\)- the maximal restriction of A(t) to \(X_{\nu}.\) Conversely, in Part II one presents a general method for the construction of ``extrapolation spaces'' and ``extrapolated operators'' which are semigroup generators. So, starting with the Cauchy problem for \(A_{\nu}\) one can find \(X_ 0\) and A(t) for which the same problem is well-posed. The paper improves previous results of the author. He gives a strong motivation of the study and carefully establishes the relations with the references.
Mathematics Subject Classification ID: 47D03
Mathematics Subject Classification ID: 46M35
Mathematics Subject Classification ID: 47F05
Mathematics Subject Classification ID: 47E05
zbMATH DE Number: 4067668
zbMATH Keywords: interpolation spaces
zbMATH Keywords: Cauchy problem
zbMATH Keywords: extrapolation spaces
zbMATH Keywords: extrapolated operators
zbMATH Keywords: semigroup generators
MaRDI profile type: Publication
full work available at URL: 0022-1236(88)90120-6
OpenAlex ID: W2029059837
cites work: Q3752735
cites work: Classical solutions of nonautonomous Riccati equations arising in parabolic boundary control problems. II
cites work: Q4726657
cites work: Q3915354
cites work: Quasilinear Evolution Equations and Parabolic Systems
cites work: Quasilinear parabolic systems under nonlinear boundary conditions
cites work: Semigroups and nonlinear evolution equations
cites work: On abstract parabolic fundamental solutions
cites work: Parabolic evolution equations and nonlinear boundary conditions
cites work: Q4112938
cites work: Equations d'évolution abstraites non linéaires de type parabolique
cites work: Maximal regularity for evolution equations by interpolation and extrapolation
cites work: Hölder regularity for non-autonomous abstract parabolic equations
cites work: Q3786959
cites work: Singular perturbation and boundary layer for an abstract Cauchy problem
cites work: Analyticity of solutions of quasilinear evolution equations. II
cites work: Q3244654
cites work: Abstract Evolution Equations of Parabolic Type in Banach and Hilbert Spaces
cites work: Q5526485
cites work: Q3291810
cites work: Q4069857
cites work: Q3775869
cites work: Interpolation Spaces Between Domains of Elliptic Operators and Spaces of Continuous Functions with Applications to Nonlinear Parabolic Equations
cites work: Semigroups of linear operators and applications to partial differential equations
cites work: The linearization principle for the stability of solutions of quasilinear parabolic equations. I
cites work: Q3669959
cites work: Equations of parabolic type in a Banach space
cites work: Q3288333
cites work: Q3278564
cites work: Q3207428
cites work: Q4169288
cites work: Q4725169
cites work: On the abstract linear evolution equations in Banach spaces
cites work: On the abstract evolution equation of parabolic type
description: scientific article; zbMATH DE number 4067668