Decay rates of the derivatives of the solutions of the heat equations in the exterior domain of a ball

摘要

Where Ω_L = {x ∈ R~N : |x| > L}, N ≥ 2, L > 0, 0 ≤ μ ≤ 1, ν is the outer unit normal vector to ∂Ω_L, and V is a nonnegative smooth function such that V(r) = O(r~(-2)) as r → ∞. In this paper, we study the decay rates of the derivatives ▽_x~j u of the solution u to (P) as t → ∞.