Local Boundary Controllability for the Semilinear Plate Equation

The problem of local controllability for the semilinear plate equation with Dirichlet boundary conditions is studied. By making use of Schauder’s fixed point theorem and the inverse function theorem, we prove that this system is locally controllable under a super-linear assumption on the nonlinearity, that is, the initial states in a small neighborhood of 0 in a certain function space can be driven to rest by Dirichlet boundary controls. Our super-linear assumption includes the critical exponent.