L. S. Pulkina, “A problem with dynamic nonlocal condition for pseudohyperbolic equation”, Izv. Vyssh. Uchebn. Zaved. Mat., 2016, no. 9, 42–50; Russian Math. (Iz. VUZ), 60:9 (2016), 38

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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2016, Number 9, Pages 42–50 (Mi ivm9150)

This article is cited in 15 scientific papers (total in 15 papers)

A problem with dynamic nonlocal condition for pseudohyperbolic equation

L. S. Pulkina

Samara National Research University, 1 Akademika Pavlova str., Samara, 443011 Russia

Full-text PDF (185 kB) Citations (15)

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Abstract: We consider an initial-boundary problem with dynamic nonlocal boundary condition for a pseudohyperbolic fourth-order equation in a cylinder. Dynamic nonlocal boundary condition represents a relation between values of a required solution, its derivatives with respect of spacial variables, second-order derivatives with respect to time variable and an integral term. The main result lies in substantiation of solvability of this problem. We prove the existence and uniqueness of a generalized solution. The proof is based on the a priori estimates obtained in this paper, Galyorkin's procedure and the properties of the Sobolev spaces.

Keywords: dynamic boundary conditions, pseudohyperbolic equation, nonlocal conditions, generalized solution.

Received: 15.02.2015

English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2016, Volume 60, Issue 9, Pages 38–45
DOI: https://doi.org/10.3103/S1066369X16090048

Bibliographic databases:

Document Type: Article

UDC: 517.956

Language: Russian

Citation: L. S. Pulkina, “A problem with dynamic nonlocal condition for pseudohyperbolic equation”, Izv. Vyssh. Uchebn. Zaved. Mat., 2016, no. 9, 42–50; Russian Math. (Iz. VUZ), 60:9 (2016), 38–45

Citation in format AMSBIB

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https://www.mathnet.ru/eng/ivm/y2016/i9/p42

This publication is cited in the following 15 articles:

M. J. Huntul, Ibrahim Tekin, “Simultaneous determination of the time‐dependent potential and force terms in a fourth‐order Rayleigh–Love equation”, Math Methods in App Sciences, 46:6 (2023), 6949
A. I. Kozhanov, R. R. Safiullova, “Ob odnom klasse psevdogiperbolicheskikh uravnenii s neizvestnym koeffitsientom”, Chelyab. fiz.-matem. zhurn., 7:2 (2022), 164–180
H. Lopushanska, A. Lopushansky, “Inverse problems for a time fractional diffusion equation in the Schwartz-type distributions”, Math. Meth. Appl. Sci., 44 (2021), 2381–2392
I. Tekin, “Determination of a time-dependent potential in a Rayleigh-Love equation with non-classical boundary condition”, Commun. Fac. Sci. Univ. Ank.-Ser, A1 Math. Stat, 70:1 (2021), 331–340
T. K. Yuldashev, B. I. Islomov, U. Sh. Ubaydullaev, “On boundary value problems for a mixed type fractional differential equation with Caputo operator”, Bull. Karaganda Univ-Math., 101:1 (2021), 127–137
A. V. Gilev, O. M. Kechina, L. S. Pulkina, “Kharakteristicheskaya zadacha dlya uravneniya chetvertogo poryadka s dominiruyuschei proizvodnoi”, Vestn. SamU. Estestvennonauchn. ser., 27:3 (2021), 14–21
A. B. Beilin, L. S. Pulkina, “Zadacha s dinamicheskim kraevym usloviem dlya odnomernogo giperbolicheskogo uravneniya”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 24:3 (2020), 407–423
V. A. Kirichek, “O gladkosti resheniya odnoi nelokalnoi zadachi dlya giperbolicheskogo uravneniya”, Vestn. SamU. Estestvennonauchn. ser., 26:2 (2020), 15–22
A. T. Assanova, Zh. S. Tokmurzin, “Boundary value problem for system of pseudo-hyperbolic equations of the fourth order with nonlocal condition”, Russian Math. (Iz. VUZ), 64:9 (2020), 1–11
L. S. Pulkina, V. A. Kirichek, “Razreshimost nelokalnoi zadachi dlya giperbolicheskogo uravneniya s vyrozhdayuschimisya integralnymi usloviyami”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 23:2 (2019), 229–245
H. Lopushanska, A. Lopushansky, “Inverse problem with a time-integral condition for a fractional diffusion equation”, Math. Meth. Appl. Sci., 42:9 (2019), 3327–3340
L. S. Pulkina, A. B. Beylin, “Nonlocal approach to problems on longitudinal vibration in a short bar”, Electron. J. Differ. Equ., 2019, 29
V. A. Kirichek, L. S. Pulkina, “Zadacha s dinamicheskimi granichnymi usloviyami dlya giperbolicheskogo uravneniya”, Vestn. SamU. Estestvennonauchn. ser., 2017, no. 1, 21–27
V. A. Kirichek, “Zadacha s nelokalnym granichnym usloviem dlya giperbolicheskogo uravneniya”, Vestn. SamU. Estestvennonauchn. ser., 2017, no. 3, 26–33
A. B. Beilin, L. S. Pulkina, “Zadacha s nelokalnymi dinamicheskimi usloviyami dlya uravneniya kolebanii tolstogo sterzhnya”, Vestn. SamU. Estestvennonauchn. ser., 2017, no. 4, 7–18

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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Russian Mathematics (Izvestiya VUZ. Matematika)

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