Backward uniqueness results for some parabolic equations in an infinite rod

Jérémi Dardé; Sylvain Ervedoza

doi:10.3934/mcrf.2019046

Article Contents

2019, Volume 9, Issue 4: 673-696. Doi: 10.3934/mcrf.2019046

This issue Previous Article Strong stabilization of (almost) impedance passive systems by static output feedback Next Article Time optimal internal controls for the Lotka-McKendrick equation with spatial diffusion

Backward uniqueness results for some parabolic equations in an infinite rod

Jérémi Dardé and
Sylvain Ervedoza^,

Institut de Mathématiques de Toulouse, UMR 5219, Université de Toulouse, CNRS, UPS IMT F-31062 Toulouse Cedex 9, France

^* Corresponding author: Sylvain Ervedoza
^* Corresponding author: Sylvain Ervedoza

Received: June 2018

Revised: August 2019

Published: November 2019

The first author is partially supported by IFSMACS ANR-15-CE40-0010 of the French National Research Agency (ANR) and both authors are supported by the CIMI Labex, Toulouse, France, under grant ANR-11-LABX-0040-CIMI

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Abstract

The goal of this article is to provide backward uniqueness results for several models of parabolic equations set on the half line, namely the heat equation, and the heat equation with quadratic potential and with purely imaginary quadratic potentials, with non-homogeneous boundary conditions. Such result can thus also be interpreted as a strong lack of controllability on the half line, as it shows that only the trivial initial datum can be steered to zero. Our results are based on the explicit knowledge of the kernel of each equation, and standard arguments from complex analysis, namely the Phragmén-Lindelöf principle.

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Mathematics Subject Classification: 35A08, 35B37, 35B53, 35K08, 93C20.

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