A unique continuation property for a class of parabolic differential inequalities in a bounded domain

This article is concerned with a strong unique continuation property of forward differential inequality abstracted from parabolic equations proposed on convex domain $ \Omega prescribed some regularity and growth conditions. Our results show that the value solutions can be determined uniquely by its an arbitrary open subset \omega in at any given positive time T $. We also derive quantitative nature this continuation, is, estimate L^2(\Omega) norm initial data, which majorized solution bounded terminal moment t =