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Mat. Zametki, 2011, Volume 90, Issue 2, Pages 254–268 (Mi mz8626)  

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

On the Solvability of Certain Spatially Nonlocal Boundary-Value Problems for Linear Hyperbolic Equations of Second Order

A. I. Kozhanov

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

Abstract: The present paper studies the solvability of spatially nonlocal boundary-value problems with Samarskii boundary condition with variable coefficients for linear hyperbolic equations of second order in the one-dimensional case. In the case of boundary conditions with constant coefficients for the equation
$$ u_{tt}-u_{xx}+c(x)u=f(x,t), $$
similar problems were studied earlier by other authors; a significant aspect of their papers was the use of the Fourier method, which dictated a special form of the equation as well as the constancy of the coefficients of the boundary conditions. The method used here does not involve such constraints and allows us to study more general problems.

Keywords: linear hyperbolic equation of second order, spatially nonlocal boundary-value problem, Samarskii boundary condition, Young's inequality

DOI: https://doi.org/10.4213/mzm8626

Full text: PDF file (509 kB)
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English version:
Mathematical Notes, 2011, 90:2, 238–249

Bibliographic databases:

UDC: 517.946
Received: 28.04.2009
Revised: 29.12.2010

Citation: A. I. Kozhanov, “On the Solvability of Certain Spatially Nonlocal Boundary-Value Problems for Linear Hyperbolic Equations of Second Order”, Mat. Zametki, 90:2 (2011), 254–268; Math. Notes, 90:2 (2011), 238–249

Citation in format AMSBIB
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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. N. E. Tokmagambetov, “Gellerstedt Equation with the Perturbation of the Cauchy Condition”, J. Math. Sci., 213:6 (2016), 910–916  mathnet  crossref
    2. Tokmagambetov N. Nalzhupbayeva G., “Operator perturbed Cauchy problem for the Gellerstedt equation”, ADVANCEMENTS IN MATHEMATICAL SCIENCES: Proceedings of the International Conference on Advancements in Mathematical Sciences (Antalya, Turkey, 5–7 November 2015), AIP Conference Proceedings, 1676, ed. Ashyralyev A. Malkowsky E. Lukashov A. Basar F., Amer Inst Physics, 2015, 020098  crossref  isi  scopus
    3. R. R. Safiullova, “On a solvability of the nonlinear inverse problem for the hyperbolic equation”, J. Math. Sci., 228:4 (2018), 431–448  mathnet  crossref  crossref
    4. Pulkina L.S., “Nonlocal Problems For Hyperbolic Equations With Degenerate Integral Conditions”, Electron. J. Differ. Equ., 2016, 193  mathscinet  zmath  isi  elib
    5. K. U. Khubiev, “Ob odnoi nelokalnoi zadache dlya uravneniya smeshannogo giperbolo-parabolicheskogo tipa”, Matematicheskie zametki SVFU, 24:3 (2017), 12–18  mathnet  crossref  elib
    6. A. I. Kozhanov, G. A. Lukina, “Nelokalnye kraevye zadachi s chastichno integralnymi usloviyami dlya vyrozhdayuschikhsya differentsialnykh uravnenii s kratnymi kharakteristikami”, Sib. zhurn. chist. i prikl. matem., 17:3 (2017), 37–51  mathnet  crossref
    7. Sofiane D., Abdelfatah B., Taki-Eddine O., “Study of Solution For a Parabolic Integrodifferential Equation With the Second Kind Integral Condition”, Int. J. Anal. Appl., 16:4 (2018), 569–593  crossref  zmath  isi
    8. Pulkina L.S., Beylin A.B., “Nonlocal Approach to Problems on Longitudinal Vibration in a Short Bar”, Electron. J. Differ. Equ., 2019, 29  mathscinet  zmath  isi
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