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Matematicheskie Zametki, 2008, Volume 84, Issue 5, Pages 693–712
DOI: https://doi.org/10.4213/mzm4078 (Mi mzm4078) 		 
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
Full-text PDF (640 kB) Citations (8)
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DOI: https://doi.org/10.4213/mzm4078
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.
Received: 06.08.2007
English version:
Mathematical Notes, 2008, Volume 84, Issue 5, Pages 646–663
DOI: https://doi.org/10.1134/S0001434608110060
Bibliographic databases:
UDC: 517.95
Language: Russian
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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  • https://doi.org/10.4213/mzm4078
  • https://www.mathnet.ru/eng/mzm/v84/i5/p693
    • This publication is cited in the following 8 articles:
    1. 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
    2. 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
    3. 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
    4. 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
    5. 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
    6. 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
    7. 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
    8. 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
    Citing articles in Google Scholar: Russian citations, English citations
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