Observation estimate for the heat equations with Neumann boundary condition via logarithmic convexity - Archive ouverte HAL Access content directly
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.
Fichier principal
Vignette du fichier
LogConvNeumann.pdf (309.4 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

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

Identifiers

Cite

Rémi Buffe, Kim Dang Phung. Observation estimate for the heat equations with Neumann boundary condition via logarithmic convexity. Journal of Evolution Equations, 2022, ⟨10.1007/s00028-022-00842-2⟩. ⟨hal-03238278⟩
427 View
105 Download

Altmetric

Share

Gmail Facebook X LinkedIn More