TITLE

APPLICATION OF MIXED FORMULATIONS OF QUASI-REVERSIBILITY TO SOLVE ILL-POSED PROBLEMS FOR HEAT AND WAVE EQUATIONS: THE 1D CASE

AUTHOR(S)
BÉCACHE, ELIANE; BOURGEOIS, LAURENT; FRANCESCHINI, LUCAS; DARDÉ, JÉRÉMI
PUB. DATE
November 2015
SOURCE
Inverse Problems & Imaging;Nov2015, Vol. 9 Issue 4, p971
SOURCE TYPE
Academic Journal
DOC. TYPE
Case Study
ABSTRACT
In this paper we address some ill-posed problems involving the heat or the wave equation in one dimension, in particular the backward heat equation and the heat/wave equation with lateral Cauchy data. The main objective is to introduce some variational mixed formulations of quasi-reversibility which enable us to solve these ill-posed problems by using some classical Lagrange finite elements. The inverse obstacle problems with initial condition and lateral Cauchy data for heat/wave equation are also considered, by using an elementary level set method combined with the quasi-reversibility method. Some numerical experiments are presented to illustrate the feasibility for our strategy in all those situations.
ACCESSION #
110721129

 

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