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

Regularization of backward parabolic equations in Banach spaces by generalized Sobolev equations Full article

Journal

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

Output data

Year: 2024, Volume: 32, Number: 1, Pages: 9-20 Pages count : 12 DOI: 10.1515/jiip-2023-0046

Tags

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

Authors

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

Affiliations

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

Submitted:	May 29, 2023
Accepted:	Jun 20, 2023
Published online:	Jul 28, 2023
Published print:	Feb 1, 2024

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

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Web of science	1
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