Local null-controllability of a two-parabolic nonlinear system with coupled boundary conditions by a neumann control

This article is concerned with the local boundary null-controll-ability of a 1-D system of two-parabolic nonlinear equations (often referred as reaction-diffusion system) with coupled boundary conditions by means of a scalar control. The control force is exerted on one of the two state components through a Neumann condition at the left end of the boundary while the other component simply satisfies the homogeneous Neumann condition at that point. On the other hand, at the right end of the boundary, the states are coupled through the so-called delta '-type condition. Upon linearization around the stationary point (0,0), we apply the well-known moments method to prove the global null-controllability of the associated linearized system with explicit control cost Me-M/T as T -> 0(+). Then, we show the local null-controllability of the main system by employing the source term method developed in [29] followed by the Banach fixed point theorem.