Stability for an inverse problem for a two-speed hyperbolic PDE in one space dimension

Suppose A(x), B(x) are 2 × 2 matrices on an interval [0, ∞) and C is a constant diagonal matrix with distinct positive entries. Let U(x, t) be the matrix solution of the system of hyperbolic PDEs CUtt − Uxx − AUx − BU = 0 on [0, ∞) x R with the initial condition U(., t) = 0 for t < 0 and the boundary condition U(0, t) = δ(t)I2. We prove a stability result for the inverse problem of recovering A, B from Ux(0,.). The solutions of the forward problem propagate with two different speeds so techniques for inverse problems for a single hyperbolic PDE are not applicable in any obvious way