Space-like strong unique continuation for some fractional parabolic equations

TL;DR

This paper proves space-like strong unique continuation for certain fractional parabolic equations using a doubling property and blowup analysis, advancing understanding of nonlocal PDE behavior.

Contribution

It introduces a novel approach combining a conditional doubling property and blowup analysis to establish unique continuation for fractional parabolic equations.

Findings

Established space-like strong unique continuation for fractional parabolic equations.

Developed a conditional elliptic doubling property for solutions.

Applied blowup analysis to prove the main theorem.

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.