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On the Existence of a Solution to the Cauchy Initial Boundary Value Problem. / Basov, V. V.; Iljin, Yu A.

In: Vestnik St. Petersburg University: Mathematics, Vol. 53, No. 2, 01.04.2020, p. 180-190.

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

Harvard

Basov, VV & Iljin, YA 2020, 'On the Existence of a Solution to the Cauchy Initial Boundary Value Problem', Vestnik St. Petersburg University: Mathematics, vol. 53, no. 2, pp. 180-190. https://doi.org/10.1134/S1063454120020053

APA

Basov, V. V., & Iljin, Y. A. (2020). On the Existence of a Solution to the Cauchy Initial Boundary Value Problem. Vestnik St. Petersburg University: Mathematics, 53(2), 180-190. https://doi.org/10.1134/S1063454120020053

Vancouver

Basov VV, Iljin YA. On the Existence of a Solution to the Cauchy Initial Boundary Value Problem. Vestnik St. Petersburg University: Mathematics. 2020 Apr 1;53(2):180-190. https://doi.org/10.1134/S1063454120020053

Author

Basov, V. V. ; Iljin, Yu A. / On the Existence of a Solution to the Cauchy Initial Boundary Value Problem. In: Vestnik St. Petersburg University: Mathematics. 2020 ; Vol. 53, No. 2. pp. 180-190.

BibTeX

@article{022f8a868ff842b89db19d8275e844b8,
title = "On the Existence of a Solution to the Cauchy Initial Boundary Value Problem",
abstract = "The initial-value problem (the Cauchy problem) for an ordinary differential equation of the first order is considered. It is assumed that the right-hand side of the equation is a continuous function defined on a set consisting of a connected open set (a domain) of the two-dimensional Euclidean space, as well as on part of its boundary. It is known that, for any point of the domain, the Peano theorem guarantees the existence of a solution to the Cauchy problem determined on the Peano segment. The sufficient conditions for the existence of a solution to the Cauchy problem set at the boundary point of the domain are formulated, and its existence at some analog of the Peano segment is proved by the Euler polygonal method. Also, the sufficient conditions for the absence of a solution to the Cauchy problem set at the boundary point are presented.",
keywords = "existence of a solution, initial boundary value problem, Peano segment",
author = "Basov, {V. V.} and Iljin, {Yu A.}",
note = "Funding Information: This work was supported by the Russian Foundation for Basic Research, project no. 19-01-00388. Publisher Copyright: {\textcopyright} 2020, Pleiades Publishing, Ltd. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.",
year = "2020",
month = apr,
day = "1",
doi = "10.1134/S1063454120020053",
language = "English",
volume = "53",
pages = "180--190",
journal = "Vestnik St. Petersburg University: Mathematics",
issn = "1063-4541",
publisher = "Pleiades Publishing",
number = "2",

}

RIS

TY - JOUR

T1 - On the Existence of a Solution to the Cauchy Initial Boundary Value Problem

AU - Basov, V. V.

AU - Iljin, Yu A.

N1 - Funding Information: This work was supported by the Russian Foundation for Basic Research, project no. 19-01-00388. Publisher Copyright: © 2020, Pleiades Publishing, Ltd. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2020/4/1

Y1 - 2020/4/1

N2 - The initial-value problem (the Cauchy problem) for an ordinary differential equation of the first order is considered. It is assumed that the right-hand side of the equation is a continuous function defined on a set consisting of a connected open set (a domain) of the two-dimensional Euclidean space, as well as on part of its boundary. It is known that, for any point of the domain, the Peano theorem guarantees the existence of a solution to the Cauchy problem determined on the Peano segment. The sufficient conditions for the existence of a solution to the Cauchy problem set at the boundary point of the domain are formulated, and its existence at some analog of the Peano segment is proved by the Euler polygonal method. Also, the sufficient conditions for the absence of a solution to the Cauchy problem set at the boundary point are presented.

AB - The initial-value problem (the Cauchy problem) for an ordinary differential equation of the first order is considered. It is assumed that the right-hand side of the equation is a continuous function defined on a set consisting of a connected open set (a domain) of the two-dimensional Euclidean space, as well as on part of its boundary. It is known that, for any point of the domain, the Peano theorem guarantees the existence of a solution to the Cauchy problem determined on the Peano segment. The sufficient conditions for the existence of a solution to the Cauchy problem set at the boundary point of the domain are formulated, and its existence at some analog of the Peano segment is proved by the Euler polygonal method. Also, the sufficient conditions for the absence of a solution to the Cauchy problem set at the boundary point are presented.

KW - existence of a solution

KW - initial boundary value problem

KW - Peano segment

UR - http://www.scopus.com/inward/record.url?scp=85085881200&partnerID=8YFLogxK

U2 - 10.1134/S1063454120020053

DO - 10.1134/S1063454120020053

M3 - Article

AN - SCOPUS:85085881200

VL - 53

SP - 180

EP - 190

JO - Vestnik St. Petersburg University: Mathematics

JF - Vestnik St. Petersburg University: Mathematics

SN - 1063-4541

IS - 2

ER -

ID: 70963496