Article Dans Une Revue SIAM Journal on Control and Optimization Année : 2016

NULL CONTROLLABILITY OF ONE-DIMENSIONAL PARABOLIC EQUATIONS BY THE FLATNESS APPROACH

Lionel Rosier
Pierre Rouchon

Résumé

We consider linear one-dimensional parabolic equations with space dependent coefficients that are only measurable and that may be degenerate or singular. Considering generalized Robin-Neumann boundary conditions at both extremities, we prove the null controllability with one boundary control by following the flatness approach, which provides explicitly the control and the associated trajectory as series. Both the control and the trajectory have a Gevrey regularity in time related to the $L^p$ class of the coefficient in front of $u_t$. The approach applies in particular to the (possibly degenerate or singular) heat equation $(a(x)u_x)_x-u_t=0$ with $a(x)>0$ for a.e. $x\in (0,1)$ and $a+1/a \in L^1(0,1)$, or to the heat equation with inverse square potential $u_{xx}+(\mu / |x|^2)u-u_t=0$ with $\mu\ge 1/4$.

Fichier principal
Vignette du fichier
PE-final-2.pdf (295.46 Ko) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)
Licence
Loading...

Dates et versions

hal-01073404 , version 1 (09-10-2014)
hal-01073404 , version 2 (01-09-2015)

Licence

Identifiants

Citer

Philippe Martin, Lionel Rosier, Pierre Rouchon. NULL CONTROLLABILITY OF ONE-DIMENSIONAL PARABOLIC EQUATIONS BY THE FLATNESS APPROACH. SIAM Journal on Control and Optimization, 2016, 54 (1), pp.198-220. ⟨hal-01073404v2⟩
745 Consultations
645 Téléchargements

Altmetric

Partager

  • More