Numerical solution of an ill-posed Cauchy problem for a quasilinear parabolic equation using a Carleman weight function
Mathematical Physics
2016-03-03 v1 math.MP
Abstract
This is the first publication in which an ill-posed Cauchy problem for a quasi- linear PDE is solved numerically by a rigorous method. More precisely, we solve the side Cauchy problem for a 1-d quasilinear parabolc equation. The key idea is to minimize a strictly convex cost functional with the Carleman Weight Function in it. Previous publications about numerical solutions of ill-posed Cauchy problems were considering only linear equations.
Keywords
Cite
@article{arxiv.1603.00848,
title = {Numerical solution of an ill-posed Cauchy problem for a quasilinear parabolic equation using a Carleman weight function},
author = {Michael V. Klibanov and Nikolaj A. Koshev and Jingzhi Li and Anatoly G. Yagola},
journal= {arXiv preprint arXiv:1603.00848},
year = {2016}
}
Comments
20 pages, 4 figures