On a time nonlocal problem for inhomogeneous evolution equations
type: Item
instance of: scholarly article
title: On a time nonlocal problem for inhomogeneous evolution equations
zbMATH Open document ID: 1320.47044
DOI: 10.1134/S0037446614040144
author: Yu. Yu. Fedorova
author: Vladimir E. Fedorov
author: Natalia D. Ivanova
published in: Siberian Mathematical Journal
publication date: 2014-12-17T00:00:00Z
review text: In this paper, the authors study the solvability of the nonlocal problem for the inhomogeneous differential evolution equation in Banach space, in which the main operator generates a strongly continuous semigroup and the determining solution is given by an integral condition in the sense of Stieltjes. They obtain necessary and sufficient conditions for the existence of a generalized solution for the problem, which depends on whether the nonlocal data belong to the generator domain. Moreover, they give some conditions for the existence of the classical solution of the nonlocal problem. Furthermore, they extend these result to a Sobolev-type linear equation in Banach space, which has a degenerate operator at the derivative. Finally, they give an example to illustrate the application of the result.
Mathematics Subject Classification ID: 47D06
Mathematics Subject Classification ID: 34B05
Mathematics Subject Classification ID: 34G10
Mathematics Subject Classification ID: 34K30
zbMATH DE Number: 6381107
zbMATH Keywords: nonlocal problem
zbMATH Keywords: operator semigroup
zbMATH Keywords: Sobolev-type equation
zbMATH Keywords: time boundary value problem
reviewed by: Gen Qi Xu
MaRDI profile type: Publication
cites work: Q3244654
cites work: Q5679204
cites work: Q3667283
cites work: Q5691484
cites work: Q3854034
cites work: Q5481988
cites work: A variational principle for linear evolution problems nonlocal in time
cites work: A problem nonlocal in time for the equations of the dynamics of a barotropic ocean
cites work: Q4812206
cites work: On a nonlocal boundary value problem with variable coefficients for the heat equation and the Aller equation
cites work: Q3684512
cites work: Theorem about the existence and uniqueness of a solution of a nonlocal abstract cauchy problem in a banach space
cites work: Linear and nonlinear nonlocal boundary value problems for differential-operator equations
cites work: On some nonlocal boundary value problems for evolution equations
cites work: Uniqueness theorems for linear non-local problems for abstract differential equations
cites work: Q4235164
cites work: Degenerate strongly continuous semigroups of operators
cites work: Q3838053
cites work: Q3623536
cites work: Q3628164
cites work: Q4983443
cites work: On solvability of perturbed Sobolev type equations
full work available at URL: s0037446614040144
OpenAlex ID: W2086211337
description: scientific article; zbMATH DE number 6381107