14:00h – 14:40h

Interacting flexible structures with localized strong damping mecha-
nisms: Semigroup stability and regularity.

14:50h – 15:30h

PARABOLIC SYSTEM WITH BOUNDARY CONDITIONS:WELL-POSEDNESS AND NULL CONTROLLABILITY

In this talk, we present some results on wellposedness and (internal
and boundary) null controllability of the parabolic equation with dynamic
boundary conditions and drift terms

∂ty − d∆y + B(x).∇y + c(x).y = 1ωu + f in ΩT ,
∂tyΓ − δ∆ΓyΓ + d∂νy + b(x).∇ΓyΓ + l(x)yΓ = 1Γ0v +g on ΓT 

y|Γ(t, x) = yΓ(t, x) on ΓT ,

y(0, ·) = y0 in Ω,
y|Γ(0, ·) = y0,Γ on Γ,
where Ω is a bounded domain of RN , with smooth boundary Γ = ∂Ω of
class C2
, ν(x) is the outer unit normal field to Ω in the point M(x) of Γ,
∂νy := (ν.∇y)|Γ, d, δ are positive real numbers, c ∈ L∞(Ω), l ∈ L∞(Γ),
B ∈ L∞(Ω)N , b ∈ L∞(Γ)N , f ∈ L2((0, T) × Ω) and g ∈ L2((0, T) × Γ). The
functions u and v are internal and boundary controls, acting on small regions ω and Γ0, respectively.
We study first the wellposedness of the above system and its associated adjoint system. To obtain boundary and null controllability, we prove adequate observability inequalities, which are obtained by establishing new internal and boundary Carleman estimates for the backward adjoint problems.