Quasi-Reversibility Method for an Ill-Posed Nonhomogeneous Parabolic Problem. (1st December 2016)

• Record Type: Journal Article
• Authors: Jana, Ajoy; Nair, M. Thamban
• Is Part Of: Numerical functional analysis and optimization. Volume 37:Number 12(2016)
• Page Start: 1529
• Page End: 1550
• Publication Date: 2016-12-01
• Subjects: Ill-posed parabolic problem -- parameter choice -- quasi-reversibility method -- regularization; 35K90 -- 47D06 -- 47A52 -- 35R25; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2016.1216448
• Languages: English
• ISSNs: 0163-0563

Abstract

ABSTRACT: The quasi-reversibility method is considered for the non-homogeneous backward Cauchy problem u t + Au = f ( t ), u ( τ ) = ϕ for 0≤ t < τ, which is known to be an ill-posed problem. Here, A is a densely defined positive self-adjoint unbounded operator on a Hilbert space H with given data f ∈ L 1 ([0, τ ], H ) and ϕ ∈ H . Error analysis is considered when the data ϕ, f are exact and also when they are noisy. The results obtained generalize and simplify many of the results available in the literature.