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 1 |
Keywords
- Decay rates estimate
- Linear parabolic equation
- Radial solutions
ASJC Scopus subject areas
- Mathematics(all)
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Ishige, K., & Kabeya, Y. (2007). Decay rates of the derivatives of the solutions of the heat equations in the exterior domain of a ball. Journal of the Mathematical Society of Japan, 59(3), 861-898. https://doi.org/10.2969/jmsj/05930861