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In this paper, we are concerned with the internal control of a class ofone-dimensional nonlinear parabolic systems with nonlocal and weakly degeneratediffusion coefficients. Our main theorem establishes a local nullcontrollability result with only one internal control for a system of twoequations. The proof, based on the ideias developed by Fursikov and Imanivilov,is obtained from the global null controllability of the linearized systemprovided by \textit{Lyusternik's Inverse Mapping Theorem}. This work extendsthe results previously treated by the authors for just one equation. For thesystem, the main issue is to obtain similar results with just one internalcontrol, which requires a new Carleman estimate with the local term justdepending on one of the state function.

Local null controllability of coupled degenerate systems with nonlocal terms and one control force