Space-like strong unique continuation for some fractional parabolic equations

Abstract

In this paper we establish the \emph{space-like} strong unique continuation for nonlocal equations of the type $({\partial }_t-\Delta {)}^{s}u=Vu$, for $0<s<1$. The proof of our main result, Theorem 1.1, is achieved via a conditional elliptic type doubling property for solutions to the appropriate extension problem, followed by a blowup analysis.