Differentiability with respect to (t,s) of the parabolic evolution operator
type: Item
instance of: scholarly article
title: Differentiability with respect to (t,s) of the parabolic evolution operator
zbMATH Open document ID: 0697.35064
DOI: 10.1007/BF02772659
author: Alessandra Lunardi
published in: Israel Journal of Mathematics
publication date: 1989-01-01T00:00:00Z
review text: The author investigates the differentiability with respect to (t,s) of the evolution operator G(t,s) associated with a time-dependent family of generators of analytic semigroups \(\{\) A(t)\(\}\) in a Banach space, having constant (but not necessarily dense) domain, and analyzes the singularity of the derivatives of G(t,s) as t approaches s. The abstract results are applied to derive representation formulae for the solution of strictly parabolic initial-boundary value problems having non-homogeneous boundary values of Dirichlet or of regular oblique derivative type.
Mathematics Subject Classification ID: 35K20
Mathematics Subject Classification ID: 35G10
Mathematics Subject Classification ID: 35K25
Mathematics Subject Classification ID: 47D03
Mathematics Subject Classification ID: 34G99
zbMATH DE Number: 4142578
zbMATH Keywords: Dirichlet
zbMATH Keywords: oblique derivative
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4142578