Author:
Banerjee Agnid,Ghosh Abhishek
Abstract
For
$s\in [\tfrac {1}{2},\, 1)$
, let
$u$
solve
$(\partial _t - \Delta )^s u = Vu$
in
$\mathbb {R}^{n} \times [-T,\, 0]$
for some
$T>0$
where
$||V||_{ C^2(\mathbb {R}^n \times [-T, 0])} < \infty$
. We show that if for some
$0<\mathfrak {K} < T$
and
$\epsilon >0$
\[ {\unicode{x2A0D}}-_{[-\mathfrak{K},\, 0]} u^2(x, t) {\rm d}t \leq Ce^{-|x|^{2+\epsilon}}\ \forall x \in \mathbb{R}^n, \]
then
$u \equiv 0$
in
$\mathbb {R}^{n} \times [-T,\, 0]$
.
Publisher
Cambridge University Press (CUP)
Reference45 articles.
1. 4 Audrito, A. and Terracini, S. . On the nodal set of solutions to a class of nonlocal parabolic reaction-diffusion equations, arXiv:1807.10135, to appear in Memoirs of AMS.
2. Hardy uncertainty principle, convexity and parabolic evolutions;Escauriaza;Commun. Math. Phys,2016
3. Decay at infinity of caloric functions within characteristic hyperplanes;Escauriaza;Math. Res. Lett,2006
4. Unique continuation property and local asymptotics of solutions to fractional elliptic equations;Fall;Commun. Partial Differ. Equ,2014
5. Quantitative uniqueness for fractional heat type operators;Arya;Calc. Var,2023