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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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\by L.~S.~Pulkina
\paper A problem with dynamic nonlocal condition for pseudohyperbolic equation
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2016
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\pages 42--50
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\issue 9
\pages 38--45
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    • This publication is cited in the following 15 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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    References:60
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