Nonexistence of global solutions for a semilinear pseudo-parabolic equations with forcing term

In present talk we consider an inhomogeneous semilinear pseudo-parabolic equation with nonlinear forcing term depending on the space variables too. Two cases are considered as a nonlinear source: the critical case of power-law nonlinearity and nonlocal nonlinearity with time integral. A result on the blowup of the solution in a finite time in the critical case is established, which answers the open question posed by Zhou (2020). In particular, this result of ours generalizes the results obtained by Bandle, Levine and Zhang (2000) for the heat equation. We also study the influence of non-local nonlinearity in time on the critical exponent and establish exact conditions for the absence of global solutions.