Multiplicative Controllability of Semilinear Parabolic Equations with Neumann Boundary Conditions

摘要

We prove the controllability and the existence of the time optimal control for semilinear parabolic equations with the homogenous Neumann boundary condition via multiplicative controls. It is worth pointing out that there is no restriction on the growth of the nonlinearity f(s) with respect to the variable s in the equation, which is a remarkable difference compared to the semilinear parabolic system with additive locally distributed controls.