The destruction of the solution of the non-local equation with gradient non-linearity

In this paper we continue our consideration of equations with gradient nonlinearities. In this paper, we consider initial-boundary value problem in a bounded domain with smooth boundary for non-local in time equation with gradient nonlinearity and prove the local solvability of the strong generalized sense, in addition, we obtain sufficient conditions for the destruction of a finite time and sufficient conditions for global in time solubility.