Decay at infinity of caloric functions within characteristic hyperplanes
Luis Escauriaza, Carlos E. Kenig, Gustavo Ponce, Luis Vega · arXiv (Cornell University) · 2005
It is shown that a function $u$ satisfying, $|Δu+\partial_tu|\le M(|u|+| abla u|)$, $|u(x,t)|\le Me^{M|x|^2}$ in $\R^n\times [0,T]$ and $|u(x,0)|\le C_ke^{-k|x|^2}$ in $\R^n$ and for all $k\ge 1$, must vanish identically in $\R^n\times [0,T]$.