A complex-analytic approach to the problem of uniform controllability of a transport equation in the vanishing viscosity limit
Glass, Olivier (2010), A complex-analytic approach to the problem of uniform controllability of a transport equation in the vanishing viscosity limit, Journal of Functional Analysis, 258, 3, p. 852-868. http://dx.doi.org/10.1016/j.jfa.2009.06.035
TypeArticle accepté pour publication ou publié
Journal nameJournal of Functional Analysis
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Abstract (EN)We revisit a result by Coron and Guerrero stating that the one-dimensional transport-diffusion equation u_x+ Mu_x-εu_xx=0 in(0,T)×(0,L) controlled by the left Dirichlet boundary value is zero-controllable at a bounded cost as ε→0+, when T>4.3L/M if M>0 and when T>57.2L/|M| if M<0. By a completely different method, relying on complex analysis, we prove that this still holds when T>4.2L/M if M>0 and when T>6.1L/|M| if M<0.
Subjects / KeywordsVanishingviscositylimit; Null controllability
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