Quasireversibility Methods for Non-Well-Posed Problems
| dc.contributor.author | Clark, Gordon W. | |
| dc.contributor.author | Oppenheimer, Seth F. | |
| dc.date.accessioned | 2018-08-17T16:27:49Z | |
| dc.date.available | 2018-08-17T16:27:49Z | |
| dc.date.issued | 1994-11-29 | |
| dc.description.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. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 9 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.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. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/7545 | |
| dc.language.iso | en | |
| dc.publisher | Southwest Texas State University, Department of Mathematics | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.source | Electronic Journal of Differential Equations, 1994, San Marcos, Texas: Southwest Texas State University and University of North Texas. | |
| dc.subject | Quasireversibility | |
| dc.subject | Final value problems | |
| dc.subject | III-posed problems | |
| dc.title | Quasireversibility Methods for Non-Well-Posed Problems | |
| dc.type | Article |