Higher Order Asymptotic Expansion for the Heat Equation with a Nonlinear Boundary Condition

• Kawakami Tatsuki

  Osaka Prefecture University

抄録

We consider the heat equation with a nonlinear boundary condition: (P) ∂_tu = Δu in R₊^N × (0,∞), ∂_νu = κ|u|^p−1u on ∂ R₊^N × (0,∞), u(x,0) = φ (x) in R₊^N, where R₊^N = {x= (x′,x_N) ∈ R^N: x_N > 0}, N ≥ 2, ∂_t = ∂/∂_t, ∂_ν = −∂/∂x_N, κ ∈ R, and p > 1 + 1/N. Let u be a solution of (P) satisfying sup_t>0(1 + t)^{(N/2)(1−1/q)}[||u(t)||_L^q(R₊^N) + t^1/(2q)||u(t)||_{L^q(∂R₊^N)}] < ∞, q ∈ [1,∞]. In this paper, under suitable assumptions of the initial function φ, we establish the method of obtaining higher order asymptotic expansions of the solution u as t → ∞.

収録刊行物

• Funkcialaj Ekvacioj

  Funkcialaj Ekvacioj 57 (1), 57-89, 2014

  日本数学会函数方程式論分科会

キーワード

• Nonlinear boundary condition
• Asymptotic expansion
• Large time behavior

詳細情報

• CRID: 1390001205111745536
• NII論文ID: 130003391680
• DOI: 10.1619/fesi.57.57
• ISSN: 05328721
• 本文言語コード: en
• データソース種別:
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  • Crossref
  • CiNii Articles
  • KAKEN
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