On the finite-time blowup of solutions to initial–boundary value problems for pseudoparabolic equations with pseudo-Laplacian

Initial–boundary value problems for pseudoparabolic equations with pseudo-Laplacian are considered. The local and global unique solvability of the problems under consideration is proved in a weakened sense. Furthermore, sufficient conditions for the blowup of solutions in a finite time are obtained. For certain problems, upper bounds are found for the blowup time of solutions. A physical interpretation of the results is presented.