Regularization strategy for the Cauchy problem of Laplace’s equation from the viewpoint of regularization theory
✍ Scribed by Ailin Qian, Jianfeng Mao
- Book ID
- 118819246
- Publisher
- Wuhan University
- Year
- 2012
- Tongue
- English
- Weight
- 409 KB
- Volume
- 17
- Category
- Article
- ISSN
- 1007-1202
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📜 SIMILAR VOLUMES
We consider the Cauchy problem for the Laplace equation in the half plane x > 0 where the Cauchy data is given at x = 0 and the solution is sought in the interval 0 < x < 1. This is a model ill-posed problem since a small perturbation in the initial data leads to large errors in the solution. We use
## Abstract The non‐characteristic Cauchy problem for the heat equation __u__~__xx__~(__x__,__t__) = __u__~1~(__x__,__t__), 0 ⩽ __x__ ⩽ 1, − ∞ < __t__ < ∞, __u__(0,__t__) = φ(__t__), __u__~__x__~(0, __t__) = ψ(__t__), − ∞ < __t__ < ∞ is regularizèd when approximate expressions for φ and ψ are given