This article is cited in 4 scientific papers (total in 4 papers)
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
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.
wave equation, power nonlinearity, Cauchy–Darboux problem, existence and the absence of a global solution, local solvability.
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Siberian Mathematical Journal, 2013, 54:6, 1120–1136
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
\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.
\jour Siberian Math. J.
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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
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
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
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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