On the blowup of solutions to semilinear pseudoparabolic equations with rapidly growing nonlinearities

The first initial-boundary value problems for nonlinear pseudoparabolic equations with rapidly growing nonlinearities are considered. The unique solvability is proved in the classical and weakened senses. In this case, in a finite amount of time, the maximum absolute value of the solution with respect to the spatial variables becomes infinite; i.e., a strong discontinuity of the solutions to the problems under consideration is formed in a finite amount of time.