A modified quasi-boundary value method for a class of abstract parabolic ill-posed problems
Boundary Value Problems volume 2006, Article number: 37524 (2006)
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.
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Denche, M., Djezzar, S. A modified quasi-boundary value method for a class of abstract parabolic ill-posed problems. Bound Value Probl 2006, 37524 (2006). https://doi.org/10.1155/BVP/2006/37524