The nal value problem,
ae u t + Au = 0 ; 0 ! t ! T u(T ) = f
with positive self-adjoint unbounded A is known to be ill-posed. One approach to dealing with this has been the method of quasireversibility, where the operator is perturbed to obtain a well-posed problem which approximates the original problem. In this work, we will use a quasi-boundary-value method, where we perturb the nal condition to form an approximate non-local problem depending on a small parameter. We show that the approximate problems are well posed and that their solutions u converge on 0; T] if and only if the original problem has a classical solution. We obtain several other results, including some explicit convergence rates.
Electronic Journal of Differential Equations
Clark, G. W., & Oppenheimer, S. F. Quasireversibility methods for non-well-posed problems. Electronic Journal of Differential Equations, 1994(8), 1-9.