Null controllability of the heat equation with boundary Fourier conditions:: The linear case

In this paper, we prove the global null controllability of the linear heat equation completed with linear Fourier boundary conditions of the form partial derivative y/partial derivative n + beta y = 0. We consider distributed controls with support in a small set and nonregular coefficients beta = beta(x, t). For the proof of null controllability, a crucial tool will be a new Carleman estimate for the weak solutions of the classical heat equation with nonhomogeneous Neumann boundary conditions.