Electron. J. Diff. Eqns., Vol. 1994(1994), No. 08, pp. 1-9.

### Quasireversibility Methods for Non-Well-Posed Problems

Gordon W. Clark & Seth F. Oppenheimer

**Abstract:**

The final value problem,

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
. We show that the approximate problems are well posed and
that their solutions
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.

Submitted November 14, 1994. Published November 29, 1994.

Math Subject Classification: 35A35, 35R25.

Key Words: Quasireversibility, Final Value Problems, Ill-Posed Problems.

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Gordon W. Clark

Department of Mathematics,
Kennesaw State College,
P O Box 444,
Marietta, GA 30061, USA

e-mail: clark@math.msstate.edu
Seth F. Oppenheimer

Department of Mathematics and Statistics,
Mississippi State University,
Drawer MA MSU, MS 39762, USA

e-mail: seth@math.msstate.edu

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