Volume 26, 2020
|Number of page(s)||30|
|Published online||13 November 2020|
Null-controllability of perturbed porous medium gas flow*
Departamento de Matemáticas, Universidad Autónoma de Madrid,
2 Chair of Computational Mathematics, Fundación Deusto, Av. de las Universidades, 24, 48007 Bilbao, Basque Country, Spain.
** Corresponding author: firstname.lastname@example.org
Accepted: 27 February 2020
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.
Mathematics Subject Classification: 93B05 / 35K65 / 93C20 / 35R35
Key words: Null-controllability / degenerate parabolic equation / porous medium equation / thin-film equation
This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No.765579-ConFlex and grant agreement No. 694126-DyCon, grant MTM2017-92996-C2-1-R COSNET of MINECO (Spain), and by the Air Force Office of Scientific Research under Award No. FA9550-18-1-0242.
© EDP Sciences, SMAI 2020
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