A complex-analytic approach to the problem of uniform controllability of a transport equation in the vanishing viscosity limit

作者：Glass Olivier^*

来源：Journal of Functional Analysis, 2010, 258(3): 852-868.

DOI：10.1016/j.jfa.2009.06.035

• Null controllability
• Vanishing viscosity limit

We revisit a result by Coron and Guerrero stating that the one-dimensional transport-diffusion equation
u(t) + Mu(x) - epsilon u(xx) = 0 in (0, T) x (0, L),
controlled by the left Dirichlet boundary value is zero-controllable at a bounded cost as epsilon -> 0(+), when T > 4.3L/M if M > 0 and when T > 57.2L/vertical bar M vertical bar 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 > 6.1 L/vertical bar M vertical bar if M < 0.

• 出版日期2010-2-1