کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4645043 1632179 2015 29 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Carleman estimates for the regularization of ill-posed Cauchy problems
ترجمه فارسی عنوان
کارلمن برای مقابله با مشکالت کوشی تخمین زده است
کلمات کلیدی
نظر سنجی، کارلمن تخمین می زند، مشکالت کوشی منفی، نرخ همگرایی
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات محاسباتی
چکیده انگلیسی

This work is a survey of results for ill-posed Cauchy problems for PDEs of the author with co-authors starting from 1991. A universal method of the regularization of these problems is presented here. Even though the idea of this method was previously discussed for specific problems, a universal approach of this paper was not discussed, at least in detail. This approach consists in constructing of such Tikhonov functionals which are generated by unbounded linear operators of those PDEs. The approach is quite general one, since it is applicable to all PDE operators for which Carleman estimates are valid. Three main types of operators of the second order are among them: elliptic, parabolic and hyperbolic ones. The key idea is that convergence rates of minimizers are established using Carleman estimates. Generalizations to nonlinear inverse problems, such as problems of reconstructions of obstacles and coefficient inverse problems are also feasible.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Applied Numerical Mathematics - Volume 94, August 2015, Pages 46–74
نویسندگان
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