Regularization of Boundary-Value Problems for Hyperbolic Equations

The problem of the stability of wave propagation in anisotropic inhomogeneous media is considered. The class of approximate solutions possessing the stability property with respect to the small deviations of the input data in the form regularizing the operators $R(\varphi,\psi,x,t,\alpha)$ is constructed. Here an important role is played by the choice of the smoothing function and by the conditions for matching the regularization parameter with the error.