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.