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Quasi-Reversibility Method for an Ill-Posed Nonhomogeneous Parabolic Problem
Published in Taylor and Francis Inc.
2016
Volume: 37
   
Issue: 12
Pages: 1529 - 1550
Abstract
The quasi-reversibility method is considered for the non-homogeneous backward Cauchy problem ut+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∈L1([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. © 2016, Copyright © Taylor & Francis Group, LLC.
About the journal
JournalData powered by TypesetNumerical Functional Analysis and Optimization
PublisherData powered by TypesetTaylor and Francis Inc.
ISSN01630563
Open AccessNo
Concepts (12)
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    Functional analysis
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    Mathematical techniques
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    CAUCHY PROBLEMS
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    ILL POSED PROBLEM
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    Nocv1
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    Non-homogeneous
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    Parabolic problems
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    PARAMETER CHOICE
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    QUASI-REVERSIBILITY METHODS
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    Regularization
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    UNBOUNDED OPERATORS
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    Laplace transforms