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Izv. Vyssh. Uchebn. Zaved. Mat., 2016, Number 9, Pages 42–50 (Mi ivm9150)  

This article is cited in 8 scientific papers (total in 8 papers)

A problem with dynamic nonlocal condition for pseudohyperbolic equation

L. S. Pulkina

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

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.

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English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2016, 60:9, 38–45

Bibliographic databases:

UDC: 517.956
Received: 15.02.2015

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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\by L.~S.~Pulkina
\paper A problem with dynamic nonlocal condition for pseudohyperbolic equation
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2016
\issue 9
\pages 42--50
\mathnet{http://mi.mathnet.ru/ivm9150}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2016
\vol 60
\issue 9
\pages 38--45
\crossref{https://doi.org/10.3103/S1066369X16090048}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84979217633}


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

    This publication is cited in the following articles:
    1. Lopushanska H., Lopushansky A., “Inverse Problems For a Time Fractional Diffusion Equation in the Schwartz-Type Distributions”, Math. Meth. Appl. Sci.  crossref  isi
    2. V. A. Kirichek, L. S. Pulkina, “Zadacha s dinamicheskimi granichnymi usloviyami dlya giperbolicheskogo uravneniya”, Vestn. SamU. Estestvennonauchn. ser., 2017, no. 1, 21–27  mathnet  elib
    3. V. A. Kirichek, “Zadacha s nelokalnym granichnym usloviem dlya giperbolicheskogo uravneniya”, Vestn. SamU. Estestvennonauchn. ser., 2017, no. 3, 26–33  mathnet  crossref  elib
    4. 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  mathnet  crossref  elib
    5. 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  mathnet  crossref  elib
    6. Lopushanska H., Lopushansky A., “Inverse Problem With a Time-Integral Condition For a Fractional Diffusion Equation”, Math. Meth. Appl. Sci., 42:9 (2019), 3327–3340  crossref  isi
    7. Pulkina L.S., Beylin A.B., “Nonlocal Approach to Problems on Longitudinal Vibration in a Short Bar”, Electron. J. Differ. Equ., 2019, 29  isi
    8. 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  mathnet  crossref
  • Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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