Estimates for the lifespan of solutions of an initial-boundary value problem for a nonlinear Sobolev equation with variable coefficient

We consider an initial-boundary value problem for a nonlinear equation of Sobolev type with variable coefficient multiplying the power-law nonlinearity. We obtain sufficient conditions for both time-global and time-local solvability. In the case of local (but not global) solvability, we find two-sided estimates for the lifespan of the solution in the form of quadrature formulas and indicate special cases in which a closed form of these estimates is possible.