Uniform controllability of a transport equation in zero fourth order equation-dispersion limit

Karim Kassab (1)

1 LJLL - Laboratoire Jacques-Louis Lions

In this paper, we study the cost of a transport equation perturbed by small diffusion and dispersion terms. When the control time is large enough, we prove that this cost decreases exponentially to zero as the diffusion and dispersion coefficients of the equation vanishes. When the control time is small, on the contrary, we prove that this cost increases exponentially to infinity.

Mots clés: Fourth order parabolic equation; Carleman estimates; cost of null controllability; boundary control; uniform null controllability; diffusion-dispersion limit

Domaines: Equations aux dérivées partielles [math.AP]

Karim Kassab. Uniform controllability of a transport equation in zero fourth order equation-dispersion limit. 2020. ⟨hal-03080969⟩