Point source identification in nonlinear advection-diffusion-reaction systems

We consider a problem of identification of point sources in time-dependent advection-diffusion systems with a nonlinear reaction term. The linear counterpart of the problem in question can be reduced to solving a system of nonlinear algebraic equations via the use of adjoint equations. We extend thi...

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Bibliographic Details
Published inInverse problems Vol. 29; no. 3; pp. 35009 - 26
Main Authors Mamonov, A V, Tsai, Y-H R
Format Journal Article
LanguageEnglish
Published IOP Publishing 01.03.2013
Subjects
Adjoints
Algebra
Algorithms
Construction
Inverse problems
Mathematical analysis
Nonlinearity
Point sources
source point identification inverse problem nonlinear advection diffusion reaction parabolic elliptic adjoint
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Summary:We consider a problem of identification of point sources in time-dependent advection-diffusion systems with a nonlinear reaction term. The linear counterpart of the problem in question can be reduced to solving a system of nonlinear algebraic equations via the use of adjoint equations. We extend this approach by constructing an algorithm that solves the problem iteratively to account for the nonlinearity of the reaction term. We study the question of improving the quality of source identification by adding more measurements adaptively using the solution obtained previously with a smaller number of measurements.
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ISSN:0266-5611
1361-6420
DOI:10.1088/0266-5611/29/3/035009