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Integrated semigroups and parabolic equations. Part I: linear perburbation of almost sectorial operators

Integrated semigroups and parabolic equations. Part I: linear perburbation of almost sectorial... The paper deals with linear abstract Cauchy problem with non-densely defined and almost sectorial operators, whenever the part of this operator in the closure of its domain is sectorial. This kind of problem naturally arises for parabolic equations with non-homogeneous boundary conditions. Using the integrated semigroup theory, we prove an existence and uniqueness result for integrated solutions. Moreover, we study the linear perturbation problem. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Evolution Equations Springer Journals

Integrated semigroups and parabolic equations. Part I: linear perburbation of almost sectorial operators

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References (32)

Publisher
Springer Journals
Copyright
Copyright © 2010 by Springer Basel AG
Subject
Mathematics; Analysis
ISSN
1424-3199
eISSN
1424-3202
DOI
10.1007/s00028-009-0049-z
Publisher site
See Article on Publisher Site

Abstract

The paper deals with linear abstract Cauchy problem with non-densely defined and almost sectorial operators, whenever the part of this operator in the closure of its domain is sectorial. This kind of problem naturally arises for parabolic equations with non-homogeneous boundary conditions. Using the integrated semigroup theory, we prove an existence and uniqueness result for integrated solutions. Moreover, we study the linear perturbation problem.

Journal

Journal of Evolution EquationsSpringer Journals

Published: May 1, 2010

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