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Mat. Zametki, 2008, Volume 84, Issue 5, Pages 693–712 (Mi mz4078)  

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

First Darboux Problem for Nonlinear Hyperbolic Equations of Second Order

O. M. Dzhokhadze, S. S. Kharibegashvili

A. Razmadze Mathematical Institute, Georgian Academy of Sciences

Abstract: We study the first Darboux problem for hyperbolic equations of second order with power nonlinearity. We consider the question of the existence and nonexistence of global solutions to this problem depending on the sign of the parameter before the nonlinear term and the degree of its nonlinearity. We also discuss the question of local solvability of the problem.

Keywords: first Darboux problem, nonlinear hyperbolic equation of second order, integral equation of Volterra type, Green–Hadamard function, Leray–Schauder theorem

DOI: https://doi.org/10.4213/mzm4078

Full text: PDF file (640 kB)
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English version:
Mathematical Notes, 2008, 84:5, 646–663

Bibliographic databases:

UDC: 517.95
Received: 06.08.2007

Citation: O. M. Dzhokhadze, S. S. Kharibegashvili, “First Darboux Problem for Nonlinear Hyperbolic Equations of Second Order”, Mat. Zametki, 84:5 (2008), 693–712; Math. Notes, 84:5 (2008), 646–663

Citation in format AMSBIB
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\paper First Darboux Problem for Nonlinear Hyperbolic Equations of Second Order
\jour Mat. Zametki
\yr 2008
\vol 84
\issue 5
\pages 693--712
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\crossref{https://doi.org/10.4213/mzm4078}
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\yr 2008
\vol 84
\issue 5
\pages 646--663
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  • http://mi.mathnet.ru/eng/mz/v84/i5/p693

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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. S. S. Kharibegashvili, O. M. Dzhokhadze, “The Cauchy–Goursat Problem for Wave Equations with Nonlinear Dissipative Term”, Math. Notes, 94:6 (2013), 913–929  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. S. S. Kharibegashvili, O. M. Dzhokhadze, “The Cauchy–Darboux problem for the one-dimensional wave equation with power nonlinearity”, Siberian Math. J., 54:6 (2013), 1120–1136  mathnet  crossref  mathscinet  isi
    3. Kharibegashvili S.S., Dzhokhadze O.M., “Second Darboux Problem for the Wave Equation with a Power-Law Nonlinearity”, Differ. Equ., 49:12 (2013), 1577–1595  crossref  mathscinet  zmath  isi  scopus
    4. Kharibegashvili S., Jokhadze O., “on a Zaremba Type Problem For Nonlinear Wave Equations in the Angular Domains”, Proc. A Razmadze Math. Inst., 167 (2015), 130–135  mathscinet  zmath  isi
    5. Kharibegashvili S.S., Jokhadze O.M., “On the solvability of a boundary value problem for nonlinear wave equations in angular domains”, Differ. Equ., 52:5 (2016), 644–666  crossref  mathscinet  zmath  isi  scopus
    6. Kharibegashvili S., Jokhadze O., “The Cauchy-Darboux Problem For Wave Equations With a Nonlinear Dissipative Term”, Mem. Differ. Equ. Math. Phys., 69 (2016), 53–75  mathscinet  zmath  isi
    7. Kharibegashvili S., Jokhadze O., “The Second Darboux Problem For the Wave Equation With Integral Nonlinearity”, Trans. A Razmadze Math. Inst., 170:3 (2016), 385–394  crossref  mathscinet  zmath  isi
    8. Kharibegashvili S., “Some Local and Nonlocal Multidimensional Problems For a Class of Semilinear Hyperbolic Equations and Systems”, Mem. Differ. Equ. Math. Phys., 75 (2018), 1–91  mathscinet  isi
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