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

2016/03/02 by Michael V. Klibanov, Nikolaj A. Koshev, Klibanov, Michael V. +5
Mathematics · Physics and Astronomy · #35R30 #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.MP #msc:35R30

paper · pdf · doi:10.48550/arxiv.1603.00848

20 pages, 4 figures

arxiv created 2016/03/02 · arxiv updated 2016/03/03

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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