Null-controllability of perturbed porous medium gas flow

Borjan Geshkovski (1)

1 UAM - Universidad Autónoma de Madrid

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.

Domaines: Mathématiques [math]; Optimisation et contrôle [math.OC]; Equations aux dérivées partielles [math.AP]

Borjan Geshkovski. Null-controllability of perturbed porous medium gas flow. 2019. ⟨hal-02280993⟩