Singular optimal control: A linear 1-D parabolic–hyperbolic example

Article type: Research Article

Authors: Coron, J.-M. | Guerrero, S.

Affiliations: Université Paris Sud and Institut universitaire de France, Département de Mathématique, bâtiment 425, 91405 Orsay, France E-mail: [email protected] | Dpto. E.D.A.N., University of Sevilla, Aptdo. 1160, 41080 Sevilla, Spain E-mail: [email protected]

Abstract: We consider the problem of the null controllability of a family of 1-D linear control parabolic equations depending on two parameters, namely the viscosity and the coefficient of the transport term. We study the dependence, with respect to these parameters and the time of controllability, of the norm of the optimal controls. In particular we give estimates on the optimal control as the viscosity tends to 0.

Journal: Asymptotic Analysis, vol. 44, no. 3-4, pp. 237-257, 2005