The linear heat equation with highly oscillating potential
İsmail Kömbe · Proceedings of the American Mathematical Society · 2004
In this paper we consider the following initial value problem: \[ { ∂ u ∂ t = − H u + V ( x ) u a m p ; in R N × ( 0 , T ) , u ( x , 0 ) = u 0 ( x ) ≥ 0 a m p ; on R N × { t = 0 } , \begin {cases} \frac {\partial u}{\partial t}=-Hu+V(x)u & \text {in $\mathbb {R}^N\times (0,T)$},\\ u(x,0) = u_0 (x)\geq 0 & \text {on $\mathbb {R}^N \times \{t=0\}$}, \end {cases} \] where H = − Δ − β | x | 2 sin ( 1 |