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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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    • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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