An iterative procedure for estimation of variable coefficients in a hyperbolic system

摘要

A parameter estimation problem for the acoustic wave equation in a multidimensional bounded domain with absorbing boundary conditions depending on the parameter is solved by using quasilinearization techniques. Results on the Fréchet differentiability of the solution with respect to the parameter are derived by applying the energy method. An iterative procedure employing quasilinearization at each iteration step is given to solve the estimation problem. Results on the convergence of the method are presented. Numerical examples illustrate the application of our algorithm.