日本大学理工学部理工学研究所研究ジャーナル
Online ISSN : 2185-4181
Print ISSN : 1884-8702
ISSN-L : 1884-8702
一般論文
Blow-up Time of Solutions for a Fast Diffusion Equation with a Variable Exponent
Takefumi IGARASHI
著者情報
キーワード: Blow-up, Fast, Diffusion, Equation, Variable
ジャーナル オープンアクセス

2015 年 2015 巻 134 号 p. 134_1-134_6

詳細
抄録
This paper is concerned with the Cauchy problem for a fast diffusion equation involving a variable exponent ut = Δum + up(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 pp(x) ≤ sup p = p+. Since the thermal conductively mum−1 ↑ ∞ when u ↓ 0, mathematically ut = Δum + up(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.
著者関連情報
© 2015 Nihon University Research Institute of Science and Technology
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