Scale-invariant extinction time estimates for some singular diffusion equations
Yoshikazu Giga - Graduate School of Mathematical Sciences, University of Tokyo, Komaba 3-8-1, Tokyo 153-8914, Japan (email)
Abstract: We study three singular parabolic evolutions: the second-order total variation flow, the fourth-order total variation flow, and a fourth-order surface diffusion law. Each has the property that the solution becomes identically zero in finite 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.
Keywords: Total variation flow, extinction time, surface diffusion.
Received: July 2010; Revised: July 2010; Available Online: February 2011.
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