Damping problem for the special class of the second order hyperbolic systems

Abstract

We consider the damping problem for the hyperbolic system with mixed derivative as the special case of boundary control problem. For different cases the given system is transformed to the triangular or diagonal form, allowing separation of equations. The corresponding transformation is applied to the initial and final data. Two components of boundary control vectors are constructed by solving the Cauchy problem for homogeneous or inhomogeneous equation. The inverse transformation gives the desired control functions.