Carleman commutator approach in logarithmic convexity for parabolic equations

Kim Dang Phung

doi:10.3934/mcrf.2018040

Article Contents

2018, Volume 8, Issue 3&4: 899-933. Doi: 10.3934/mcrf.2018040

This issue Previous Article Recurrence for switching diffusion with past dependent switching and countable state space Next Article Controllability under positivity constraints of semilinear heat equations

Carleman commutator approach in logarithmic convexity for parabolic equations

Kim Dang Phung

Institut Denis Poisson, CNRS, UMR 7013, Université d’Orléans, BP 6759, 45067 Orléans Cedex 2, France

Received: August 2017

Revised: December 2017

Published: September 2018

This work is supported by the Région Centre (France) - THESPEGE Project

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Abstract

In this paper we investigate on a new strategy combining the logarithmic convexity (or frequency function) and the Carleman commutator to obtain an observation estimate at one time for the heat equation in a bounded domain. We also consider the heat equation with an inverse square potential. Moreover, a spectral inequality for the associated eigenvalue problem is derived.

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Mathematics Subject Classification: Primary: 35K05, 35K65; Secondary: 35B60, 35P20.

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