LAUSR

Abstract We show that the Moore–Gibson–Thomson equation τ ∂ t t t y + α ∂ t t y − c 2 Δ y − b Δ ∂ t y = k ∂ t t ( 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 − τ c 2 b > 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.