Supersolutions for a class of nonlinear parabolic systems

Kazuhiro Ishige, Tatsuki Kawakami, Mikołaj Sierzȩga

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)6084-6107
Number of pages24
JournalJournal of Differential Equations
Volume260
Issue number7
DOIs
Publication statusPublished - 2016 Apr 5

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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