Uniform controllability of scalar conservation laws in the vanishing viscosity limit

Matthieu Léautaud 1, 2
1 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
Inria Saclay - Ile de France, UMA - Unité de Mathématiques Appliquées, CNRS - Centre National de la Recherche Scientifique : UMR7231
Abstract : We deal with viscous perturbations of scalar conservation laws on a bounded interval with a general flux function f and a small dissipation coefficient Ɛ. Acting on this system on both endpoints of the interval, we prove global exact controllability to constant states with nonzero speed. More precisely, we construct boundary controls so that the solution is driven to the targeted constant state, and we moreover require these controls to be uniformly bounded as Ɛ → 0+ in an appropriate space. For general (nonconvex) flux functions this can be done for sufficiently large time, and for convex fluxes f, we have a precise estimate on the minimal time needed to control. © 2012 Society for Industrial and Applied Mathematics.
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SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, 2012, 50 (3), pp.1661-1699. 〈10.1137/100803043〉
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Soumis le : mardi 6 août 2013 - 09:46:47
Dernière modification le : jeudi 11 janvier 2018 - 06:20:23

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Matthieu Léautaud. Uniform controllability of scalar conservation laws in the vanishing viscosity limit. SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, 2012, 50 (3), pp.1661-1699. 〈10.1137/100803043〉. 〈hal-00849559〉

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