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This paper is devoted to deriving global Carleman estimate for a one-dimensional linear coupled parabolic system of m equations with bounded variations (BV) diffusion coefficients. This kind of estimate is a generalization of the scalar result (Le Rousseau in J. Differ. Equ. 233:417-447, 2007). The key ingredient is to derive a global Carleman estimate for piecewise-C1Open image in new window diffusion coefficients based on the construction of a suitable weight function. The Carleman estimate in the case of BV diffusion coefficients is then obtained using the approach of BV diffusion coefficients by piecewise-constant coefficients. This Carleman estimate is used to show the observability inequality which yields the controllability result.

Carleman estimate for a one-dimensional system of m coupled parabolic PDEs with BV diffusion coefficients