Abstract
We consider the initial-boundary value problem (p) {∂/∂tu = Δu - V(|x|)u in ΩL × (0,∞), μu + (1 - μ)∂/∂vu = 0 on ∂ΩL × (0, ∞), u(·, 0) = ø(·) ∈ Lp(ΩL), p ≥ 1, where ΩL = {x ∈N : |x| > L}, N ≥ 2, L > 0, 0 ≤ μ ≤ 1, v is the outer unit normal vector to ∂ΩL, 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 ▽xju of the solution u to (P) as t → ∞.
Original language | English |
---|---|
Pages (from-to) | 861-898 |
Number of pages | 38 |
Journal | Journal of the Mathematical Society of Japan |
Volume | 59 |
Issue number | 3 |
DOIs | |
Publication status | Published - 2007 Jul |
Externally published | Yes |
Keywords
- Decay rates estimate
- Linear parabolic equation
- Radial solutions
ASJC Scopus subject areas
- Mathematics(all)