DETERMINATION OF A TIME - DEPENDENT TERM IN THE RIGHT HAND SIDE OF LINEAR PARABOLIC EQUATIO NS WITH ROBIN BOUNDARY CONDITION FROM BOUNDARY OBSERVATIONS

Abstract

We propose a variational method for determining a time-dependent term in the right hand side of parabolic equations with Robin boundary condition from boundary observations. We have shown the formula for functional to be minimized gradient via an adjoint problem. The direct problem is discretized by the finite difference methods and the variational problem is solved by the conjugate gradient method and Tikhonov regularization.