Controllability Results for the Moore–Gibson–Thompson Equation Arising in Nonlinear Acoustics

We show that the Moore–Gibson–Thomson equation τ∂ ttt y+α∂ tt y−c 2 Δy−bΔ∂ t y=k∂ tt (y 2 )+χ ω(t) u, is controlled by a force that is supported on an moving subset ω(t) of the domain, satisfying a geometrical condition. Using the concept of approximately outer invertible map, a generalized implicit function theorem and assuming that γ:=α−[Formula presented]>0, the local null controllability in the nonlinear case is established. Moreover, the analysis of the critical value γ=0 for the linear equation is included. © 2018 Elsevier Inc.