RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Forthcoming papers Archive Impact factor Subscription Guidelines for authors License agreement Submit a manuscript Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Mat. Zametki: Year: Volume: Issue: Page: Find

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

First Darboux Problem for Nonlinear Hyperbolic Equations of Second Order

O. M. Dzhokhadze, S. S. Kharibegashvili

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)
References: PDF file   HTML file

English version:
Mathematical Notes, 2008, 84:5, 646–663

Bibliographic databases:

UDC: 517.95

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
\Bibitem{DzhKha08} \by O.~M.~Dzhokhadze, S.~S.~Kharibegashvili \paper First Darboux Problem for Nonlinear Hyperbolic Equations of Second Order \jour Mat. Zametki \yr 2008 \vol 84 \issue 5 \pages 693--712 \mathnet{http://mi.mathnet.ru/mz4078} \crossref{https://doi.org/10.4213/mzm4078} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2500636} \transl \jour Math. Notes \yr 2008 \vol 84 \issue 5 \pages 646--663 \crossref{https://doi.org/10.1134/S0001434608110060} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000262855600006} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-59749095112} 

• http://mi.mathnet.ru/eng/mz4078
• https://doi.org/10.4213/mzm4078
• http://mi.mathnet.ru/eng/mz/v84/i5/p693

 SHARE:

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
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
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
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
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
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
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
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
•  Number of views: This page: 397 Full text: 140 References: 52 First page: 15