On a Certain Nonlinear Nonlocal Sobolev-Type Wave Equation

The initial boundary-value problem for the nonlinear nonlocal Sobolev equation is studied. Sufficient conditions for local and for global (with respect to time) solvability are obtained. For the case of local (not global) solvability, upper and lower bounds for the lifespan of the solution are obtained in the form of explicit and implicit formulas.