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

Kazuhiro Ishige, Yoshitsugu Kabeya

Research output: Contribution to journalArticle

7 Citations (Scopus)

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(·) ∈ LpL), 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 languageEnglish
Pages (from-to)861-898
Number of pages38
JournalJournal of the Mathematical Society of Japan
Volume59
Issue number3
DOIs
Publication statusPublished - 2007 Jul 1

Keywords

  • Decay rates estimate
  • Linear parabolic equation
  • Radial solutions

ASJC Scopus subject areas

  • Mathematics(all)

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