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. <i>Electronic Journal of Differential Equations, 1994</i>(08), pp. 1-9.

Rights

Attribution 4.0 International

Rights Holder

Rights License