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Pré-Publication, Document De Travail Année : 2023

Null controllability of quasilinear parabolic equations with gradient dependent coefficients

Nicolae Cindea
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Geoffrey Lacour
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Résumé

The aim of this paper is to study the null controllability of a large class of quasilinear parabolic equations. In a first step we prove that the associated linear parabolic equations with non-constant diffusion coefficients are approximately null controllable by the means of regular controls and that these controls depend continuously to the diffusion coefficient. A fixed-point strategy is employed in order to prove the null approximate controllability for the considered quasilinear parabolic equations. We also show the exact null controllability in arbitrary small time for a class of parabolic equations including the parabolic $p$-Laplacian with $\frac{3}{2} < p < 2$. The theoretical results are numerically illustrated combining a fixed point algorithm and a reformulation of the controllability problem for linear parabolic equation as a mixed-formulation which is numerically solved using a finite elements method.
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Dates et versions

hal-04060082 , version 1 (12-04-2023)
hal-04060082 , version 2 (08-09-2023)

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Nicolae Cindea, Geoffrey Lacour. Null controllability of quasilinear parabolic equations with gradient dependent coefficients. 2023. ⟨hal-04060082v1⟩
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