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Journal Articles Journal of Evolution Equations Year : 2022

Observation estimate for the heat equations with Neumann boundary condition via logarithmic convexity

Abstract

We prove an inequality of Hölder type traducing the unique continuation property at one time for the heat equation with a potential and Neumann boundary condition. The main feature of the proof is to overcome the propagation of smallness by a global approach using a refined parabolic frequency function method. It relies with a Carleman commutator estimate to obtain the logarithmic convexity property of the frequency function.
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Dates and versions

hal-03238278 , version 1 (27-05-2021)

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Rémi Buffe, Kim Dang Phung. Observation estimate for the heat equations with Neumann boundary condition via logarithmic convexity. Journal of Evolution Equations, 2022. ⟨hal-03238278⟩
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