Identification of Discontinuous Parameters in Flow Equations
Semion Gutman · SIAM Journal on Control and Optimization · 1990
A problem of identifying possibly discontinuous diffusion coefficients in parabolic equations is considered. General theorems on existence and convergence of Galerkin approximations are proved in $L^1 $ setting. Classes of functions of bounded variation are discussed and the variation estimates are obtained. A double-discretization method with the variations constraints is used in two- and three-dimensional problems and the numerical experiments are presented.