S. S. Kharibegashvili, O. M. Dzhokhadze, “The Cauchy–Darboux problem for the one-dimensional wave equation with power nonlinearity”, Sibirsk. Mat. Zh., 2013, Volume 54, Number 6,Pages <nobr>1407

This article is cited in 4 papers

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

S. S. Kharibegashvili^a, O. M. Dzhokhadze^b

^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.

UDC: 517.956.35

Received: 31.07.2012