Integraded semigroups and integrodifferential equations
type: Item
instance of: scholarly article
title: Integraded semigroups and integrodifferential equations
zbMATH Open document ID: 0682.47022
DOI: 10.1007/BF02570889
published in: Mathematische Zeitschrift
publication date: 1990-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/183786
review text: We consider the integral equation \[ (1)\quad du/dt=A(u(t))+\int^{t}_{0}B(t-s)u(s)ds+f(t) \] and, as a corollary, the abstract Cauchy problem \[ (2)\quad v^{(n+1)}(t)=A(v^{(n)}(t))+\sum^{n}_{j=1}B_ jv^{(n- j)}(t)+g(t), \] where the domain of A is contained in a domain of B(r) (r\(\geq 0)\) and \(B_ j\) (1\(\leq j\leq n)\), all operators are linear, on a Banach space, and A generates a k-times integrated semigroup, for sme \(k\in {\mathbb{N}}\cup \{0\}\). We use C-semigroups to give sufficient conditions for (1) and (2) to be well-posed, and construct the solutions.
Mathematics Subject Classification ID: 47D06
Mathematics Subject Classification ID: 47G10
zbMATH DE Number: 4117279
zbMATH Keywords: integral equation
zbMATH Keywords: abstract Cauchy problem
zbMATH Keywords: integrated semigroup
zbMATH Keywords: C- semigroups
author: R. deLaubenfels
MaRDI profile type: Publication
cites work: Resolvent Positive Operators
cites work: Vector-valued Laplace transforms and Cauchy problems
cites work: Q3830008
cites work: Q3896020
cites work: Semigruppi regolarizzabili
cites work: The Cauchy Problem and a Generalization of the Hille-Yosida Theorem
cites work: Integrated semigroups, C-semigroups and the abstract Cauchy problem
cites work: Q3728621
cites work: Propagation of singularities for integrodifferential equations
cites work: Some considerations for linear integrodifferential equations
cites work: Wellposedness and wave propagation for a class of integrodifferential equations in Banach space
cites work: Q3333539
cites work: Q3721264
cites work: Resolvent Operators for Integral Equations in a Banach Space
cites work: Series Expansions for Resolvents of Volterra Integrodifferential Equations in Banach Space
cites work: Analytic resolvent operators for integral equations in Banach space
cites work: Wave propagation for linear integrodifferential equations in Banach space
cites work: Q3742210
cites work: An integrodifferential equation for rigid heat conductors with memory
cites work: Q4183783
cites work: On the generators of exponentially bounded C-semigroups
cites work: A generalization of the Hille-Yosida theorem
cites work: Exponentially bounded C-semigroups and generation of semigroups
cites work: Exponentially bounded C-semigroups and integrated semigroups
cites work: One-parameter semigroups of positive operators
cites work: Towards a ``Matrix theory'' for unbounded operator matrices
cites work: The spectrum of unbounded operator matrices with non-diagonal domain
cites work: Well-Posedness of Higher Order Abstract Cauchy Problems
cites work: Integrated semigroups and their applications to the abstract Cauchy problem
cites work: Integrated semigroups and their application to complete second order Cauchy problems
cites work: Semigroups of linear operators and applications to partial differential equations
cites work: On the exponentially bounded C-semigroups
description: scientific article; zbMATH DE number 4117279