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UNIFORM CONTROLLABILITY OF A TRANSPORT EQUATION IN ZERO DIFFUSION–DISPERSION LIMIT

OLIVIER GLASS

UPMC Univ. Paris 06, UMR 7598 Laboratoire Jacques-Louis Lions, Paris, F-75005, France

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and

SERGIO GUERRERO

UPMC Univ. Paris 06, UMR 7598 Laboratoire Jacques-Louis Lions, Paris, F-75005, France

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https://doi.org/10.1142/S0218202509003899Cited by:17 (Source: Crossref)

Abstract

In this paper, we consider the controllability of a transport equation perturbed by small diffusion and dispersion terms. We prove that for a sufficiently large time, the cost of the null-controllability tends to zero exponentially as the perturbation vanishes. For small times, on the contrary, we prove that this cost grows exponentially.

Keywords:

AMSC: 93B05, 93C20, 35B25

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