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Preprints, Working Papers, ... Year : 2020

QUANTITATIVE RAPID AND FINITE TIME STABILIZATION OF THE HEAT EQUATION

Shengquan Xiang
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Abstract

The null controllability of the heat equation is known for decades [21, 25, 34]. The finite time stabilizability of the one dimensional heat equation was proved by Coron-Nguyên [15], while the same question for high dimensional spaces remained widely open. Inspired by Coron-Trélat [16] we find explicit stationary feedback laws that quantitatively exponentially stabilize the heat equation with decay rate λ and exp(C\sqrt{λ}) estimates, where Lebeau-Robbiano's spectral inequality [34] is naturally used. Then a piecewise controlling argument leads to null controllability with optimal cost C exp(C/T), as well as finite time stabilization.
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Dates and versions

hal-03053731 , version 1 (11-12-2020)

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  • HAL Id : hal-03053731 , version 1

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Shengquan Xiang. QUANTITATIVE RAPID AND FINITE TIME STABILIZATION OF THE HEAT EQUATION. 2020. ⟨hal-03053731⟩
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