Some control problems for the Burgers equation

Peng Gao

doi:10.1216/rmj.2020.50.559

Abstract

We show the existence of insensitizing controls and study null controllability with constraints for the Burgers equation. We solve these problems by first considering the linearized problem, then, by the Kakutani fixed point theorem, we show that the same results hold for the Burgers equation. The main difficulty in this paper is dealing with the nonlinear term in the Burgers equation.

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Peng Gao. "Some control problems for the Burgers equation." Rocky Mountain J. Math. 50 (2) 559 - 581, April 2020. https://doi.org/10.1216/rmj.2020.50.559

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Received: 31 December 1969; Revised: 25 September 2019; Accepted: 7 October 2019; Published: April 2020

First available in Project Euclid: 29 May 2020

zbMATH: 07210979

MathSciNet: MR4104394

Digital Object Identifier: 10.1216/rmj.2020.50.559

Subjects:

Primary: 35K20 , 35K55 , 93B05 , 93B07

Keywords: Burgers equation , constraints on the state , Controllability , insensitizing control , observability

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