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arXiv · 1603.00848

Numerical solution of an ill-posed Cauchy problem for a quasilinear parabolic equation using a Carleman weight function

Michael V. Klibanov·Nikolaj A. Koshev·Jingzhi Li·Anatoly G. Yagola
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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.

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Michael V. Klibanov, Nikolaj A. Koshev, Jingzhi Li, Anatoly G. Yagola. 2016-03-02. Numerical solution of an ill-posed Cauchy problem for a quasilinear parabolic equation using a Carleman weight function. https://arxiv.org/abs/1603.00848

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