Supersolutions for a class of nonlinear parabolic systems

Kazuhiro Ishige, Tatsuki Kawakami, Mikołaj Sierzȩga

研究成果: Article査読

21 被引用数 (Scopus)

抄録

In this paper, by using scalar nonlinear parabolic equations, we construct supersolutions for a class of nonlinear parabolic systems including{∂tu=δu+vp,x∈Ω,t>0,∂tv=δv+uq,x∈Ω,t>0,u=v=0,x∈∂Ω,t>0,(u(x,0),v(x,0))=(u0(x),v0(x)),x∈Ω, where p≥0, q≥0, Ω is a (possibly unbounded) smooth domain in RN and both u0 and v0 are nonnegative and locally integrable functions in Ω. The supersolutions enable us to obtain optimal sufficient conditions for the existence of the solutions and optimal lower estimates of blow-up rate of the solutions.

本文言語English
ページ(範囲)6084-6107
ページ数24
ジャーナルJournal of Differential Equations
260
7
DOI
出版ステータスPublished - 2016 4月 5

ASJC Scopus subject areas

  • 分析
  • 応用数学

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