Analyticity of solutions to parabolic evolutions and applications

TL;DR

This paper establishes new quantitative estimates on the space-time analyticity of solutions to linear parabolic equations with analytic coefficients and applies these results to derive observability inequalities and null-controllability over measurable sets.

Contribution

It provides novel quantitative analyticity estimates and demonstrates their application in control theory for parabolic evolutions.

Findings

New estimates on space-time analyticity near initial time

Observability inequalities for parabolic equations over measurable sets

Null-controllability results derived from analyticity estimates

Abstract

We find new quantitative estimates on the space-time analyticity of solutions to linear parabolic equations with analytic coefficients near the initial time. We apply the estimates to obtain observability inequalities and null-controllability of parabolic evolutions over measurable sets.