A modified quasi-boundary value method for a class of abstract parabolic ill-posed problems

A modified quasi-boundary value method for a class of abstract parabolic ill-posed problems

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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 google pixel 7 freedom final condition, we obtain an approximate nonlocal problem depending on a small parameter.

We show that the approximate problems are well posed here 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.