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

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概要

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• We consider the initial-boundary value problem (P) {$¥frac{∂}{∂t}$u = Δu-V(|x|)u   in ΩL×(0,∞), μu+(1-μ)$¥frac{∂}{∂ν}$u = 0   on ∂ΩL×(0,∞), u(·,0) = φ(·)∈Lp(ΩL),   p≥1,where ΩL={x∈RN:|x|>L}, N≥2, L>0, 0≤μ≤1, &\nu; 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→∞.

• 2007-07-01

著者

• Kabeya Yoshitsugu

  Department Of Mathematical Sciences Faculty Of Engineering Osaka Prefecture University

• Kabeya Yoshitsugu

  Department Of Applied Mathematics Faculty Of Engineering

• ISHIGE Kazuhiro

  Mathematical Institute Tohoku University

関連論文

• Number of zeros of solutions to singular initial value problems
• Decay rates of the derivatives of the solutions of the heat equations in the exterior domain of a ball
• Asymptotic behaviors of least-energy solutions to Matukuma type equations with an inverse square potential
• Uniqueness of nodal rapidly-decaying radial solutions to a linear elliptic equation on R^n
• Behavior of least-energy solutions to Matukuma type equations

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