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In this work we prove the exact controllability of the wave equation by acting on a strategic zone of the border of a non-convex polygonal domain with crack. Indeed, by combining two methods: that of Grisvard on the exact controllability on domains with corners and that of EL. Jai on the boundary strategic actutors, this exact controllability result has been proven.doi:10.9734/jamcs/2020/v35i630294 fatcat:xo2jhbyykfcnzp7asmwadketlu