Identification of a dissipation coefficient by a variational method

A generalized inverse problem for the identification of the absorption coefficient for a hyperbolic system is considered. The well-posedness of the problem is examined. It is proved that the regular part of the solution is an $L_2$ function, which reduces the inverse problem to minimizing the error functional. The gradient of the functional is determined in explicit form from the adjoint problem, and approximate formulas for its calculation are derived. A regularization algorithm for the solution of the inverse problem is considered. Numerical results obtained for various excitation sources are displayed.