Inverse Source Problem For A Class Of Wave Equation With Variable Coefficients

In this paper, we are concerned an inverse source problem for the following wave equa-tion with variable coefficients. where G (?)Rn is a bounded domain with C2 boundary (?)G, a(x)> 0, T> 0.The inverse problem discussed in this paper is to determine the source term f by some suitable boundary observation. In order to solve this inverse problem, we first derive a new Carleman estimate for the above wave equation. By using the new Carleman estimate, we proved the uniqueness and Lipschitz stability for the inverse problem with some suitable assumptions on a and f.