Null-controllability of perturbed porous medium gas flow

Geshkovski, Borjan

ESAIM: Control, Optimisation and Calculus of Variations, Tome 26 (2020), article no. 85

Suite au passage du modèle économique de la revue en S20, le texte intégral des articles des années 2019 et 2020 est accessible uniquement sur le site de l'éditeur et est réservé aux abonnés.

In this work, we investigate the null-controllability of a nonlinear degenerate parabolic equation, which is the equation satisfied by a perturbation around the self-similar solution of the porous medium equation in Lagrangian-like coordinates. We prove a local null-controllability result for a regularized version of the nonlinear problem, in which singular terms have been removed from the nonlinearity. We use spectral techniques and the source-term method to deal with the linearized problem and the conclusion follows by virtue of a Banach fixed-point argument. The spectral techniques are also used to prove a null-controllability result for the linearized thin-film equation, a degenerate fourth order analog of the problem under consideration.

Classification : 93B05, 35K65, 93C20, 35R35
Keywords: Null-controllability, degenerate parabolic equation, porous medium equation, thin-film equation

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