Global uniqueness of a multidimensional inverse problem for a nonlinear parabolic equation by a Carleman estimate

An inverse problem with the single measurement datum for a nonlinear parabolic equation in n -D is considered. The unknown coefficient q ( u , y ) depends on the solution u and ( n − 1) spatial variables y = ( x 2 , ..., x n ). Such problems were not studied in the past for n ⩾ 2. A global uniqueness result is proved by the method of Carleman estimates.