Scale-invariant extinction time estimates for some singular diffusion equations

Yoshikazu Giga, Robert Kohn

Research output: Contribution to journalArticle

Abstract

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
Volume30
Issue number2
DOIs
StatePublished - Jun 2011

Fingerprint

Extinction Time
Singular Equation
Surface diffusion
Scale Invariant
Total Variation
Diffusion equation
Fourth Order
Surface Diffusion
Energy Estimates
Estimate
Zero

Keywords

  • extinction time
  • surface diffusion
  • Total variation ow

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics
  • Analysis

Cite this

Scale-invariant extinction time estimates for some singular diffusion equations. / Giga, Yoshikazu; Kohn, Robert.

In: Discrete and Continuous Dynamical Systems, Vol. 30, No. 2, 06.2011, p. 509-535.

Research output: Contribution to journalArticle

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