Convergence of the Kato approximants for evolution equations involving functional perturbations
type: Item
instance of: scholarly article
title: Convergence of the Kato approximants for evolution equations involving functional perturbations
zbMATH Open document ID: 0531.34048
DOI: 10.1016/0022-0396(83)90041-4
published in: Journal of Differential Equations
publication date: 1983-01-01T00:00:00Z
review text: This paper is concerned with the nonlinear functional differential equation \[ (*)\quad u'(t)+A(t)u(t)=F(t,u_ t),\quad 0\leq t\leq T,\quad u_ 0=\phi \in C^ 1([-r,0];X) \] in a uniformly smooth Banach space X. Here each A(t) is m-accretive and F is Lipschitzian. It is shown that under a certain time dependence condition on A(t) the unique solution to (*) is the uniform limit of the sequence \(\{u_ n\}\) where each \(u_ n\), \(n=1,2,...\), is the solution of (*) with A(t) replaced by its Yosida approximation \(A_ n(t)=A(t)(I+(1/n)A(t))^{-1}.\)
reviewed by: Simeon Reich
Mathematics Subject Classification ID: 34G20
Mathematics Subject Classification ID: 47H06
Mathematics Subject Classification ID: 47J05
zbMATH DE Number: 3842317
zbMATH Keywords: m-accretive operator
zbMATH Keywords: nonlinear functional differential equation
zbMATH Keywords: uniformly smooth Banach space
zbMATH Keywords: Yosida approximation
author: Athanassios G. Kartsatos
author: Mary E. Parrott
MaRDI profile type: Publication
full work available at URL: 0022-0396(83)90041-4
OpenAlex ID: W2072877571
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description: scientific article; zbMATH DE number 3842317