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

Результат исследований: Вклад в журналСтатьярецензирование

11 Цитирования (Scopus)

Аннотация

We solve numerically the side Cauchy problem for a 1-D parabolic equation. The initial condition is unknown. This is an ill-posed problem. The main difference with previous results is that our equation is quasilinear, whereas known publications on this topic work only with linear PDEs. The key idea is to minimize a weighted Tikhonov functional with the Carleman Weight Function (CWF) in it. Roughly, given a reasonable bounded set of any size in a reasonable Hilbert space, one can choose the parameter of the CWF in such a way that this functional becomes strictly convex on that set.

Язык оригиналаАнглийский
Страницы (с-по)761-776
Число страниц16
ЖурналJournal of Inverse and Ill-Posed Problems
Том24
Номер выпуска6
DOI
СостояниеОпубликовано - 1 дек. 2016
Опубликовано для внешнего пользованияДа

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