NDLI: Inverse problems for linear parabolic equations using mixed formulations – Part 1: Theoretical analysis

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Inverse problems for linear parabolic equations using mixed formulations – Part 1: Theoretical analysis

Content Provider	Scilit
Author	Münch, Arnaud Souza, Diego A.
Copyright Year	2017
Description	We consider the reconstruction of the solution of a parabolic equation posed in $Ω\times(0,T) , with a bounded open subset Ω ofℝN , from a partial distributed observation. We employ a least-squares technique and minimize theL2 -norm of the distance from the observation to any solution. Taking the parabolic equation as the main constraint, the optimality conditions are reduced to a mixed formulation involving both the state to reconstruct and a Lagrange multiplier. The well-posedness of this mixed formulation, in particular the inf-sup property, is a consequence of classical energy estimates. We then reproduce the arguments to a linear first-order system, involving the normal flux, equivalent to the linear parabolic equation. The method, valid in any spatial dimension N, may also be employed to reconstruct solutions from boundary observations. With respect to the hyperbolic case, the parabolic situation requires, due to regularization properties, the introduction of an appropriate weight function so as to make the reconstruction stable with respect to standard Sobolev spaces.$
Related Links	http://arxiv.org/pdf/1508.07854
ISSN	09280219
e-ISSN	15693945
DOI	10.1515/jiip-2015-0112
Journal	Journal of Inverse and Ill-Posed Problems
Issue Number	4
Volume Number	25
Language	English
Publisher	Walter de Gruyter GmbH
Publisher Date	2017-01-01
Access Restriction	Open
Subject Keyword	Journal: Journal of Inverse and Ill-Posed Problems Journal of Inverse and Ill-posed Problems Applied Mathematics Inverse Problem Heat Equation Lagrangian Variational Formulation Carleman Estimate
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics

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