Space like strong unique continuation for sublinear parabolic equations

In this paper, we establish space like strong unique continuation property for uniformly parabolic sublinear equations under appropriate structural assumptions. Our main result Theorem 1.1 constitutes the parabolic counterpart of the strong unique continuation result recently established in (Ruland, J. Differential Equations 265 (2018) 6009–6035) for elliptic sublinear equations with analogous structure conditions. Similar to that in (Ruland, J. Differential Equations 265 (2018) 6009–6035), this is accomplished via a new (Formula presented.) type Carleman estimate for a class of sublinear parabolic operators.