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Null controllability of the heat equation with boundary Fourier conditions: the linear case. (English) Zbl 1106.93009
Summary: In this paper, we prove the global null controllability of the linear heat equation completed with linear Fourier boundary conditions of the form y n+βy=0. We consider distributed controls with support in a small set and nonregular coefficients β=β(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.
MSC:
93B05Controllability
35K20Second order parabolic equations, initial boundary value problems
49J20Optimal control problems with PDE (existence)