Scale-invariant extinction time estimates for some singular diffusion equations

Yoshikazu Giga; Robert V. Kohn

doi:10.3934/dcds.2011.30.509

Scale-invariant extinction time estimates for some singular diffusion equations

Yoshikazu Giga, Robert V. Kohn

Mathematics

Research output: Contribution to journal › Article › peer-review

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 language	English (US)
Pages (from-to)	509-535
Number of pages	27
Journal	Discrete and Continuous Dynamical Systems
Volume	30
Issue number	2
DOIs	https://doi.org/10.3934/dcds.2011.30.509
State	Published - Jun 2011

Keywords

Total variation ow
extinction time
surface diffusion

ASJC Scopus subject areas

Analysis
Discrete Mathematics and Combinatorics
Applied Mathematics

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10.3934/dcds.2011.30.509

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KW - surface diffusion

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Scale-invariant extinction time estimates for some singular diffusion equations

Abstract

Keywords

ASJC Scopus subject areas

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