Nonlocal Cauchy problems for semilinear evolution equations
type: Item
instance of: scholarly article
title: Nonlocal Cauchy problems for semilinear evolution equations
zbMATH Open document ID: 1009.34052
DOI: 10.1016/S0362-546X(01)00743-X
author: R. Smith
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2002-08-25T00:00:00Z
review text: Here, the authors study the existence and uniqueness of mild and classical solutions to nonlocal Cauchy problems for semilinear evolution equations. They first establish an existence and uniqueness result for the continuous solution to a general convolution integral equation in a Banach space and then apply this to yield existence and uniqueness results for mild and classical solutions to nonlocal Cauchy problems for semilinear evolution equations. An example which illustrates the theoretical results is also presented.
Mathematics Subject Classification ID: 34G20
zbMATH DE Number: 1788002
zbMATH Keywords: nonlocal Cauchy problem
zbMATH Keywords: semilinear evolution equation
zbMATH Keywords: convolution integralequation
zbMATH Keywords: regularized semigroups
zbMATH Keywords: fractional powers
reviewed by: Sotiris K. Ntouyas
MaRDI profile type: Publication
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full work available at URL: s0362-546x(01)00743-x
OpenAlex ID: W2154745208
description: scientific article; zbMATH DE number 1788002