A Conditional Stability Theorem in the Problem of Determining the Dispersion Index and Relaxation for the Stationary Transport Equation

We consider the problem of determining the relaxation $\sigma(x)$, $x\in\mathbb R^3$, and the dispersion index $K(x,\nu\cdot\nu')$ of the transport equation. As information for determining them, we specify emanating radiation on the boundary of a physical domain which is a function of a point on the boundary, the angular variables $\theta_0$ and $\varphi_0$ defining the acute-directed radiation incident on the boundary, and the angular variables $\theta$ and $\varphi$ defining the direction of emanating radiation. Assuming that the functions $\sigma(x)$ and $K(x,z)$ are small, we establish a stability estimate for a solution to this problem.