Finite-time blow-up for solutions to a degenerate drift-diffusion equation for a fast-diffusion case

Masaki Kurokiba, Takayoshi Ogawa

Research output: Contribution to journalArticlepeer-review

Abstract

We consider the non-existence of a time global solution to the Cauchy problem of a degenerate drift-diffusion system with a fast-diffusion exponent. We show that the solution for fast-diffusion cases with the diffusion exponent n/n+2 < α < 1 blows up in a finite time if the initial data satisfy certain conditions involving the free energy. We also show the finite-time blow-up for the radially symmetric case without a finite moment condition.

Original languageEnglish
Pages (from-to)2073-2093
Number of pages21
JournalNonlinearity
Volume32
Issue number6
DOIs
Publication statusPublished - 2019 May 8

Keywords

  • degenerate drift-diffusion system, finite-time blow-up, Shannon's inequality, existence of weak solution, free energy, virial law

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Applied Mathematics

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