The Parameter Estimation Problem for Parabolic Equations and Discontinuous Observation Operators

Parameter estimation problems are studied for a class of linear autonomous parabolic partial differential equations with various fit-to-data criteria, which may be discontinuous with respect to the state variable. We analyze the convergence of Galerkin schemes approximating the optimization problems and generalize results to higher dimensional problems. An example is then presented for the case of point observation fit-to-data criteria in higher dimensions. Finally, discretization of coefficients is discussed for identification problems with variable coefficients.