Global Uniqueness and Stability for a Class of Multidimensional Inverse Hyperbolic Problems with Two Unknowns

In this paper we obtain the global uniqueness and stability estimate for a class of multidimensional inverse hyperbolic problems of determining a source term and an initial value from a single measurement of boundary values or interior values. By means of a suitable transformation, we reduce the problem to the observability inequalities for nonconservative hyperbolic equations with memory. Then, using a compactness/uniqueness argument, we can prove the uniqueness and the stability by a new kind of unique continuation property of a nonlocal hyperbolic equation.