Heat equation with a nonlinear boundary condition and uniformly local Lr spaces

Kazuhiro Ishige, Ryuichi Sato

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)

Abstract

We establish the local existence and the uniqueness of solutions of the heat equation with a nonlinear boundary condition for the initial data in uniformly local Lr spaces. Furthermore, we study the sharp lower estimates of the blow-up time of the solutions with the initial data λψ as λ → 0 or λ → ∞ and the lower blow-up estimates of the solutions.

Original languageEnglish
Pages (from-to)2627-2652
Number of pages26
JournalDiscrete and Continuous Dynamical Systems- Series A
Volume36
Issue number5
DOIs
Publication statusPublished - 2016 May

Keywords

  • Blow-up rate
  • Blow-up time
  • Heat equation
  • Nonlinear boundary condition
  • Uniformly local L spaces

ASJC Scopus subject areas

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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