Abstract
Abstract We consider a multidimensional analogue of the Darboux problem for wave equations with power nonlinearity. Depending on the spatial dimension of an equation, a power nonlinearity exponent and the sign in front of a nonlinear term, it is proved that the Darboux problem is globally solvable in some cases, but has no global solution in other cases though the local solvability of this problem remains in force.
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