On a comparison theorem for parabolic equations with nonlinear boundary conditions

Kosuke Kita*, Mitsuharu Ôtani

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


In this article, a new type of comparison theorem for some second-order nonlinear parabolic systems with nonlinear boundary conditions is given, which can cover classical linear boundary conditions, such as the homogeneous Dirichlet or Neumann boundary condition. The advantage of our comparison theorem over the classical ones lies in the fact that it enables us to compare two solutions satisfying different types of boundary conditions. As an application of our comparison theorem, we can give some new results on the existence of blow-up solutions of some parabolic equations and systems with nonlinear boundary conditions.

Original languageEnglish
Pages (from-to)1165-1181
Number of pages17
JournalAdvances in Nonlinear Analysis
Issue number1
Publication statusPublished - 2022 Jan 1


  • blow up
  • comparison theorem
  • nonlinear boundary conditions

ASJC Scopus subject areas

  • Analysis


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