  In the present paper, we consider the parabolic and hyperbolic inequalities
with a singular potentials and with a critical nonlinearities in the annulus
domain. The problems are studied with Neumann-type and Dirichlet-type boundary
conditions on the boundary. Moreover, we study the systems of problems too. We
have proved that the above problems are globally unsolvable in critical cases,
thereby filling the gaps the recent results by Jleli and Samet in [J. Math.
Anal. Appl. 514: 2 (2022)] and in [Anal. Math. Phys. 12: 90 (2022)]. Proofs are
carried out using the method of test functions with logarithmic arguments,
which is being developed for the first time in bounded domains.
