Scale-Invariant Extinction Time Estimates for Some Singular Diffusion Equations

We study three singular parabolic evolutions: the second-order total variation ow, the fourth-order total variation ow, and a fourth-order surface diusion 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.

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