Inhomogeneous degenerate Sobolev type equations with delay
type: Item
instance of: scholarly article
title: Inhomogeneous degenerate Sobolev type equations with delay
zbMATH Open document ID: 1257.47045
DOI: 10.1134/S0037446612020152
author: E. A. Omelchenko
author: Vladimir E. Fedorov
published in: Siberian Mathematical Journal
publication date: 2012-11-14T00:00:00Z
review text: The aim of the paper is to study the existence of a unique mild solution to the delayed Sobolev type operator equation \[ L\dot{u}(t) = Mu(t) + \Phi u_t + f(t), \qquad t\in [0, \infty), \] where \(L: X\to Y\) is a continuous linear operator between Banach spaces \(X\) and \(Y\), \(M : D(M)\to Y\) is a linear, closed and densely defined operator on \(X\), and the delay operator \(\Phi : {\mathcal C}([-r, 0];X)\to Y\) is linear and continuous. For this, the authors use the methods of the theory of degenerate semigroups which are developed for studying Sobolev type equations, along with a semigroup approach to deal with delay equations.
reviewed by: Ruhollah Jahanipur
Mathematics Subject Classification ID: 47D06
Mathematics Subject Classification ID: 34K06
zbMATH DE Number: 6105684
zbMATH Keywords: Sobolev type equation
zbMATH Keywords: delay differential equation
zbMATH Keywords: semigroup of operators
MaRDI profile type: Publication
cites work: Q3623536
cites work: Q4218533
cites work: Linear Sobolev type equations and degenerate semigroups of operators
cites work: Q5806127
cites work: Elliptic functional differential equations and applications
cites work: Q5293000
cites work: Linear equations of the Sobolev type with relatively \(p\)-radial operators
cites work: Degenerate strongly continuous semigroups of operators
cites work: One-Parameter Semigroups for Linear Evolution Equations
cites work: Q4983443
cites work: On solvability of perturbed Sobolev type equations
description: scientific article; zbMATH DE number 6105684