Null Controllability For Semilinear Parabolic Equations In Non-cylindrical Domains

We consider space-time domains such that, for all t > 0, their cross section at t can be transformed from a reference domain Ω, by means of a C~2-diffeomorphism Τ_t : Ω —> Ω_t. We also assume a C~1 dependence of the domain Ω_t with respect to time. The reference domain is assumed to be a bounded open set of R~N with boundary Γ of class C~2. We investigate in this paper the null controllability for the semilinear parabolic equations in non-cylindrical domains. The fixed point method is used in the proof.