%0 Journal Article
%T A modified quasi-boundary value method for a class of abstract parabolic ill-posed problems
%A M. Denche
%A S. Djezzar
%J Boundary Value Problems
%D 2006
%I Springer
%R 10.1155/bvp/2006/37524
%X We study a final value problem for first-order abstract differential equation with positive self-adjoint unbounded operator coefficient. This problem is ill-posed. Perturbing the final condition, we obtain an approximate nonlocal problem depending on a small parameter. We show that the approximate problems are well posed and that their solutions converge if and only if the original problem has a classical solution. We also obtain estimates of the solutions of the approximate problems and a convergence result of these solutions. Finally, we give explicit convergence rates.
%U http://dx.doi.org/10.1155/BVP/2006/37524