Variational Inequalities with a Constraint on the Solution for Abstract Hyperbolic Equations

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Variational Inequalities with a Constraint on the Solution for Abstract Hyperbolic Equations. / Artyushin, A. N.

In: Siberian Mathematical Journal, Vol. 67, No. 3, 25.06.2026, p. 517-530.

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

BibTeX

@article{84adfffec13643fa814ba90bd66d81ac,

title = "Variational Inequalities with a Constraint on the Solution for Abstract Hyperbolic Equations",

abstract = "Variational inequalities with a constraint on the solution for abstract hyperbolic equations are considered.An existence theorem for a solution is proved by the penalty method.Sufficient geometric conditions on the constraint set are given that guarantee the convergence of penalized solutions to a solution to the problem.Under some additional conditions, the strong convergence of approximate solutions is proved.As a result, a solution is obtained for which the law of conservation of energy holds, which corresponds to a perfectly elastic impact.",

keywords = "abstract hyperbolic equations, variational inequalities, вариационные неравенства, абстрактные гиперболические уравнения",

author = "Artyushin, {A. N.}",

note = "Artyushin, A. N. Variational Inequalities with a Constraint on the Solution for Abstract Hyperbolic Equations / A. N. Artyushin // Siberian Mathematical Journal. – 2026. – Vol. 67, No. 3. – P. 517-530. – DOI 10.1134/S0037446626030018. – EDN AZSXIJ.",

year = "2026",

month = jun,

day = "25",

doi = "10.1134/S0037446626030018",

language = "English",

volume = "67",

pages = "517--530",

journal = "Siberian Mathematical Journal",

issn = "0037-4466",

publisher = "Pleiades Publishing",

number = "3",

}

RIS

TY - JOUR

T1 - Variational Inequalities with a Constraint on the Solution for Abstract Hyperbolic Equations

AU - Artyushin, A. N.

N1 - Artyushin, A. N. Variational Inequalities with a Constraint on the Solution for Abstract Hyperbolic Equations / A. N. Artyushin // Siberian Mathematical Journal. – 2026. – Vol. 67, No. 3. – P. 517-530. – DOI 10.1134/S0037446626030018. – EDN AZSXIJ.

PY - 2026/6/25

Y1 - 2026/6/25

N2 - Variational inequalities with a constraint on the solution for abstract hyperbolic equations are considered.An existence theorem for a solution is proved by the penalty method.Sufficient geometric conditions on the constraint set are given that guarantee the convergence of penalized solutions to a solution to the problem.Under some additional conditions, the strong convergence of approximate solutions is proved.As a result, a solution is obtained for which the law of conservation of energy holds, which corresponds to a perfectly elastic impact.

AB - Variational inequalities with a constraint on the solution for abstract hyperbolic equations are considered.An existence theorem for a solution is proved by the penalty method.Sufficient geometric conditions on the constraint set are given that guarantee the convergence of penalized solutions to a solution to the problem.Under some additional conditions, the strong convergence of approximate solutions is proved.As a result, a solution is obtained for which the law of conservation of energy holds, which corresponds to a perfectly elastic impact.

KW - abstract hyperbolic equations

KW - variational inequalities

KW - вариационные неравенства

KW - абстрактные гиперболические уравнения

UR - https://www.mendeley.com/catalogue/d8d63a3b-943a-3863-9d02-9b53d1dbe886/

UR - https://elibrary.ru/item.asp?id=91538044

UR - https://www.scopus.com/pages/publications/105042813359

U2 - 10.1134/S0037446626030018

DO - 10.1134/S0037446626030018

M3 - Article

VL - 67

SP - 517

EP - 530

JO - Siberian Mathematical Journal

JF - Siberian Mathematical Journal

SN - 0037-4466

IS - 3

ER -

ID: 84799862