Observations from measurable sets and applications
L. Escauriaza, S. Montaner, C. Zhang
TL;DR
This paper establishes new quantitative estimates on the space-time analyticity of solutions to linear parabolic equations with time-independent coefficients and uses these estimates to derive observability inequalities over measurable sets.
Contribution
It introduces novel quantitative analyticity estimates and applies them to improve observability inequalities for linear parabolic equations over measurable sets.
Findings
New quantitative estimates on space-time analyticity.
Improved observability inequalities for solutions over measurable sets.
Applications to control theory and inverse problems.
Abstract
We find new quantitative estimates on the space-time analyticity of solutions to linear parabolic equations with time-independent coefficients and apply them to obtain observability inequalities for its solutions over measurable sets.
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Taxonomy
TopicsStability and Controllability of Differential Equations · Advanced Mathematical Modeling in Engineering · Numerical methods in inverse problems