In this paper, we study the null controllability of degenerate semilinear cascade parabolic systems with one control force. The key tool is the Carleman estimates developed recently for degenerate one dimension parabolic equations. We develop a Carleman estimate for these systems and then an observability inequality for the linear adjoint system. We conclude by linearization and fixed point arguments.
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El Mustapha Ait Ben Hassi, Farid Ammar Khodja, Abdelkarim Hajjaj, Lahcen Maniar, Null controllability of degenerate parabolic cascade systems. Port. Math. 68 (2011), no. 3, pp. 345–367DOI 10.4171/PM/1895