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Regularization of backward parabolic equations in Banach spaces by generalized Sobolev equations Научная публикация

Журнал

Journal of Inverse and Ill-Posed Problems
ISSN: 0928-0219 , E-ISSN: 1569-3945

Вых. Данные

Год: 2024, Том: 32, Номер: 1, Страницы: 9-20 Страниц : 12 DOI: 10.1515/jiip-2023-0046

Ключевые слова

Backward parabolic equations; ill-posed problems; regularization; Sobolev equation

Авторы

Duc Nguyen Van ¹ , Hào Dinh Nho ² , Shishlenin Maxim ^3,4,5

Организации

1	Department of Mathematics, Vinh University, Vinh City, Vietnam
2	Hanoi Institute of Mathematics, VAST, 18 Hoang Quoc Viet Road, 10307 Hanoi, Vietnam
3	Institute of Computational Mathematics and Mathematical Geophysics
4	Sobolev Institute of Mathematics, 4 Koptyuga Prospect, Novosibirsk, Russia
5	Novosibirsk State University, Novosibirsk, Russia

Let X be a Banach space with norm || center dot || Let A : D(A) subset of X -> X be an (possibly unbounded) operator that generates a uniformly bounded holomorphic semigroup. Suppose that epsilon > 0 and T > 0 are two given constants. The backward parabolic equation of finding a function u : [ 0, T] -> X satisfying u(t) + Au = 0, 0 < t < T, ||u(T)-phi|| <= epsilon, for phi in X, is regularized by the generalized sobolev equation where 0 < alpha < 1 and A alpha = A(I + alpha A(b))(-1) with b >= 1. Error estimate of the method with respect to the noise level are proved.

Duc N.V. , Hào D.N. , Shishlenin M.
Regularization of backward parabolic equations in Banach spaces by generalized Sobolev equations
Journal of Inverse and Ill-Posed Problems. 2024. V.32. N1. P.9-20. DOI: 10.1515/jiip-2023-0046 WOS Scopus РИНЦ OpenAlex

Поступила в редакцию:	29 мая 2023 г.
Принята к публикации:	20 июн. 2023 г.
Опубликована online:	28 июл. 2023 г.
Опубликована в печати:	1 февр. 2024 г.

Web of science:	WOS:001035544500001
Scopus:	2-s2.0-85167398066
РИНЦ:	62292616
OpenAlex:	W4385303012

БД	Цитирований
OpenAlex	1
Web of science	1
Scopus	1