Critical exponents for the fast diffusion equation with a nonlinear boundary condition

Ryuichi Sato, Jin Takahashi

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper we consider the fast diffusion equation ∂tu=Δ(um) (x∈Ω, t>0) with a nonlinear boundary condition ∂νum=up (x∈∂Ω, t>0), where 0<m<1, p>0, Ω⊂RN is a smooth domain and N≥1. We prove that p0=(m+1)/2 is the critical global existence exponent for the cases Ω=RN∖B1‾ (N≥2) and Ω=B1:={x∈RN:|x|<1} (N≥1).

Original languageEnglish
Article number123526
JournalJournal of Mathematical Analysis and Applications
Volume482
Issue number1
DOIs
Publication statusPublished - 2020 Feb 1

Keywords

  • Blow-up
  • Critical exponents
  • Fast diffusion equation
  • Nonlinear boundary condition

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Fingerprint

Dive into the research topics of 'Critical exponents for the fast diffusion equation with a nonlinear boundary condition'. Together they form a unique fingerprint.

Cite this