Quasireversibility Methods for Non-Well-Posed Problems
Date
1994-11-29
Authors
Clark, Gordon W.
Oppenheimer, Seth F.
Journal Title
Journal ISSN
Volume Title
Publisher
Southwest Texas State University, Department of Mathematics
Abstract
The final value problem {
ut + Au = 0 , 0 < t < T
u(T) = ƒ
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 final condition to form an approximate non-local problem depending on a small parameter α. We show that the approximate problems are well posed and that their solutions uα 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.
Description
Keywords
quasireversibility, final value problems, iII-posed problems
Citation
Clark, G. W. & Oppenheimer, S. F. (1994). Quasireversibility Methods for Non-Well-Posed Problems. Electronic Journal of Differential Equations, 1994(08), pp. 1-9.
Rights
Attribution 4.0 International