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Scale-invariant extinction time estimates for some singular diffusion equations

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  • 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.
    Mathematics Subject Classification: Primary: 35K15, 35K30; Secondary: 35K55, 35B40.


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