Scale-invariant extinction time estimates for some singular diffusion equations

Yoshikazu Giga, Robert V. Kohn

Research output: Contribution to journalArticlepeer-review


We study three singular parabolic evolutions: the second-order total variation ow, the fourth-order total variation ow, and a fourth-order surface diffusion law. Each has the property that the solution becomes identically zero in nite time. We prove scale-invariant estimates for the extinction time, using a simple argument which combines an energy estimate with a suitable Sobolev-type inequality.

Original languageEnglish (US)
Pages (from-to)509-535
Number of pages27
JournalDiscrete and Continuous Dynamical Systems
Issue number2
StatePublished - Jun 2011


  • Total variation ow
  • extinction time
  • surface diffusion

ASJC Scopus subject areas

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics


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