Unique Solvability of a Linear Parabolic Problem with Nonlocal Time Data

V. N. Starovoitov

doi:10.1134/S0037446621020129

Unique Solvability of a Linear Parabolic Problem with Nonlocal Time Data

V. N. Starovoitov

Applied Mathematics Section

Research output: Contribution to journal › Article › peer-review

Abstract

We consider a problem for a first-order differential equationin a Hilbert space. We replace the initial data with some condition that includes the integralof the solution over the entire time interval on which we solve the problem.It is proved that the problem has a unique solution on an arbitrary time intervalunder the condition that some of the data are positive.

Original language	English
Pages (from-to)	337-340
Number of pages	4
Journal	Siberian Mathematical Journal
Volume	62
Issue number	2
DOIs	https://doi.org/10.1134/S0037446621020129
Publication status	Published - Mar 2021

Keywords

517.954
differential equation in a Hilbert space
nonlocal time data
solvability
uniqueness of solution

OECD FOS+WOS

1.01 MATHEMATICS

Access to Document

10.1134/S0037446621020129

Cite this

@article{14205a2469da40f488065f6dbf97877c,

title = "Unique Solvability of a Linear Parabolic Problem with Nonlocal Time Data",

abstract = "We consider a problem for a first-order differential equationin a Hilbert space. We replace the initial data with some condition that includes the integralof the solution over the entire time interval on which we solve the problem.It is proved that the problem has a unique solution on an arbitrary time intervalunder the condition that some of the data are positive.",

keywords = "517.954, differential equation in a Hilbert space, nonlocal time data, solvability, uniqueness of solution",

author = "Starovoitov, {V. N.}",

year = "2021",

month = mar,

doi = "10.1134/S0037446621020129",

language = "English",

volume = "62",

pages = "337--340",

journal = "Siberian Mathematical Journal",

issn = "0037-4466",

publisher = "MAIK NAUKA/INTERPERIODICA/SPRINGER",

number = "2",

}

TY - JOUR

T1 - Unique Solvability of a Linear Parabolic Problem with Nonlocal Time Data

AU - Starovoitov, V. N.

PY - 2021/3

Y1 - 2021/3

N2 - We consider a problem for a first-order differential equationin a Hilbert space. We replace the initial data with some condition that includes the integralof the solution over the entire time interval on which we solve the problem.It is proved that the problem has a unique solution on an arbitrary time intervalunder the condition that some of the data are positive.

AB - We consider a problem for a first-order differential equationin a Hilbert space. We replace the initial data with some condition that includes the integralof the solution over the entire time interval on which we solve the problem.It is proved that the problem has a unique solution on an arbitrary time intervalunder the condition that some of the data are positive.

KW - 517.954

KW - differential equation in a Hilbert space

KW - nonlocal time data

KW - solvability

KW - uniqueness of solution

UR - http://www.scopus.com/inward/record.url?scp=85103990490&partnerID=8YFLogxK

U2 - 10.1134/S0037446621020129

DO - 10.1134/S0037446621020129

M3 - Article

AN - SCOPUS:85103990490

VL - 62

SP - 337

EP - 340

JO - Siberian Mathematical Journal

JF - Siberian Mathematical Journal

SN - 0037-4466

IS - 2

ER -