Volume 29, 2023
|Number of page(s)||34|
|Published online||26 April 2023|
Local null controllability of a quasi-linear system and related numerical experiments
EDAN and IMUS, Universidad de Sevilla, Spain
2 UFPB, João Pessoa, Brazil
3 Instituto de Matemática e Estatística, Universidade Federal Fluminense, Niterói, RJ, Brazil
4 Departamento de Ciência e Tecnologia, Universidade Federal Rural do Semi-Árido, Caraúbas, RN, Brazil
* Corresponding author: firstname.lastname@example.org
Accepted: 19 January 2023
This paper concerns the null control of quasi-linear parabolic systems where the diffusion coefficient depends on the gradient of the state variable. In our main theoretical result, with some assumptions on the regularity and growth of the diffusion coefficient and regular initial data, we prove that local null controllability holds. To this purpose, we consider the null controllability problem for the linearized system, we deduce new estimates on the control and the state and, then, we apply a Local Inversion Theorem. We also formulate an iterative algorithm of the quasi-Newton kind for the computation of a null control and an associated state. We apply this method to some numerical approximations of the problem and illustrate the results with several experiments.
Mathematics Subject Classification: 35K55 / 35K59 / 90C53 / 93C20
Key words: Quasi-linear parabolic equations / nonlinear diffusion / null controllability / quasi-Newton algorithms
© The authors. Published by EDP Sciences, SMAI 2023
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