Minimal solutions of a semilinear elliptic equation with a dynamical boundary condition

Marek Fila, Kazuhiro Ishige, Tatsuki Kawakami

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)

Abstract

We study properties of positive solutions of a semilinear elliptic equation with a linear dynamical boundary condition. We establish the semigroup property for minimal solutions, show that every local-in-time solution can be extended globally, and reveal a relationship between minimal solutions of the time-dependent problem and minimal solutions of a corresponding stationary problem.

Original languageEnglish
Pages (from-to)788-809
Number of pages22
JournalJournal des Mathematiques Pures et Appliquees
Volume105
Issue number6
DOIs
Publication statusPublished - 2016 Jun 1

Keywords

  • Dynamical boundary condition
  • Minimal solutions
  • Phragmén-Lindelöf theorem
  • Semilinear elliptic equation

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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