Blow-up Time of Solutions for a Fast Diffusion Equation with a Variable Exponent

• IGARASHI Takefumi

  Department of General Education, College of Science and Technology, Nihon University

抄録

This paper is concerned with the Cauchy problem for a fast diffusion equation involving a variable exponent u_t = Δu^m + u^p(x) in Rⁿ, where m is a constant such that max{0, 1 − 2/n} < m < 1 and p(x) is a continuous bounded function such that 1 < p⁻ = inf p ≤ p(x) ≤ sup p = p⁺. Since the thermal conductively mu^m−1 ↑ ∞ when u ↓ 0, mathematically u_t = Δu^m + u^p(x) represents a fast diffusion with source. The initial condition u₀(x) is assumed to be continuous, nonnegative and bounded. For the non-decaying initial data at space infinity, any nontrivial nonnegative solutions blow up in finite time. We give the upper bound of the blow-up time of positive solutions of a fast diffusion equation for the non-decaying initial data at space infinity.

収録刊行物

• 日本大学理工学部理工学研究所　研究ジャーナル

  日本大学理工学部理工学研究所　研究ジャーナル 2015 (134), 134_1-134_6, 2015

  日本大学理工学部理工学研究所

キーワード

• Blow-up
• Fast
• Diffusion
• Equation
• Variable

詳細情報

• CRID: 1390001205338702464
• NII論文ID: 130005111221
• NII論文ID: 40020592988
• NII書誌ID: AA12464241
• DOI: 10.11346/cstj.2015.134_1
• ISSN: 21854181
• ISSN: 18848702
• NDL書誌ID: 026748464
• Web Site: http://id.ndl.go.jp/bib/026748464
• Web Site: https://ndlsearch.ndl.go.jp/books/R000000004-I026748464
• 本文言語コード: en
• データソース種別:
  • JaLC
  • NDL
  • CiNii Articles
• 抄録ライセンスフラグ: 使用不可