Operational calculus approach to PDE arising in QR-regularisation of ill-posed problems
✍ Scribed by I.H. Dimovski; S.L. Kalla; I. Ali
- Publisher
- Elsevier Science
- Year
- 2002
- Tongue
- English
- Weight
- 793 KB
- Volume
- 35
- Category
- Article
- ISSN
- 0895-7177
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✦ Synopsis
In the method of quasireversibility (QR), ill-posed problems for linear partial differential equations are replaced by well-posed problems for equations of twice-higher order. In this paper, we consider two problems: the first for the backward heat equation, and the second for a nonparabolic evolution equation. These problems are treated analytically using operational calculus intended for boundary value problems . We show that an appropriate operational approach allows us to extend the Duhamel principle to treat such problems and to obtain their solutions in closed form. (~) 2002 Elsevier Science Ltd. All rights reserved.