The degenerate drift-diffusion system with the sobolev critical exponent

Takayoshi Ogawa

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

We consider the drift-di usion system of degenerated type. For n ≥ 3, {equation presented} where > 1 and κ = 1. There exists a critical exponent that classifies the global behavior of the weak solution. In particular, we consider the critical case α* = 2n/n+2 = (2*)', where the Talenti function U(x) solving -2*ΔUn-2/n+2 = U in R n classifies the global existence of the weak solution and finite blow-up of the solution.

Original languageEnglish
Pages (from-to)875-886
Number of pages12
JournalDiscrete and Continuous Dynamical Systems - Series S
Volume4
Issue number4
DOIs
Publication statusPublished - 2011 Aug 1

Keywords

  • Blow-up
  • Degenerate drift-diffusion
  • Global weak solution
  • Sobolev critical

ASJC Scopus subject areas

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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