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 Sibirsk. Mat. Zh., 2013, Volume 54, Number 6, Pages 1407–1426 (Mi smj2506)

The Cauchy–Darboux problem for the one-dimensional wave equation with power nonlinearity

S. S. Kharibegashvilia, O. M. Dzhokhadzeb

a Georgian Technical University, Tbilisi, Georgia
b Ivane Javakhishvili Tbilisi State University, Tbilisi, Georgia

Abstract: The questions are studied of existence and uniqueness of a global solution to the Cauchy–Darboux problem for the one-dimensional wave equation with power nonlinearity. Under consideration are the existence of local solutions and the absence of global solutions.

Keywords: wave equation, power nonlinearity, Cauchy–Darboux problem, existence and the absence of a global solution, local solvability.

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English version:
Siberian Mathematical Journal, 2013, 54:6, 1120–1136

Bibliographic databases:

UDC: 517.956.35

Citation: S. S. Kharibegashvili, O. M. Dzhokhadze, “The Cauchy–Darboux problem for the one-dimensional wave equation with power nonlinearity”, Sibirsk. Mat. Zh., 54:6 (2013), 1407–1426; Siberian Math. J., 54:6 (2013), 1120–1136

Citation in format AMSBIB
\Bibitem{KhaDzh13} \by S.~S.~Kharibegashvili, O.~M.~Dzhokhadze \paper The Cauchy--Darboux problem for the one-dimensional wave equation with power nonlinearity \jour Sibirsk. Mat. Zh. \yr 2013 \vol 54 \issue 6 \pages 1407--1426 \mathnet{http://mi.mathnet.ru/smj2506} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3184105} \transl \jour Siberian Math. J. \yr 2013 \vol 54 \issue 6 \pages 1120--1136 \crossref{https://doi.org/10.1134/S0037446613060190} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000329110700019} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84891295981} 

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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. Kharibegashvili, O. Jokhadze, “On a Zaremba type problem for nonlinear wave equations in the angular domains”, Proc. A Razmadze Math. Inst., 167 (2015), 130–135
2. S. S. Kharibegashvili, O. M. Jokhadze, “On the solvability of a boundary value problem for nonlinear wave equations in angular domains”, Differ. Equ., 52:5 (2016), 644–666
3. G. Dekanoidze, S. Kharibegashvili, “On the global solvability of the first Darboux problem for one class of nonlinear second order hyperbolic systems”, Mem. Differ. Equ. Math. Phys., 71 (2017), 51–68
4. G. Dekanoidze, “On the solvability of a boundary value problem with Dirichlet and Poincaré conditions in the angular domain for one class of nonlinear second order hyperbolic systems”, Mem. Differ. Equ. Math. Phys., 71 (2017), 151–154
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