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Identification of two unknown coefficients in an integrodifferential hyperbolic equation

We prove a (local in time) existence and uniqueness theorem for the identification of two unknown coefficients q and h in a hyperbolic integrodifferential equation. The coefficient h is the so-called relaxation kernel, it is assumed to depend on time only, and q may be either an unknown term appearing in the source or the zero-order coefficient of an elliptic second-order differential operator related to a cylindrical spatial domain.