The inverse problem of reconstructing reaction–diffusion systems
Barbara Kaltenbacher, William Rundell
Abstract
Abstract This paper considers the inverse problem of recovering state-dependent source terms in a reaction–diffusion system from overposed data consisting of the values of the state variables either at a fixed finite time (census-type data) or a time trace of their values at a fixed point on the boundary of the spatial domain. We show both uniqueness results and the convergence of an iteration scheme designed to recover these sources. This leads to a reconstructive method and we shall demonstrate its effectiveness by several illustrative examples.
Topics & Concepts
MathematicsInverse problemUniquenessConvergence (economics)TRACE (psycholinguistics)Applied mathematicsFixed pointBoundary (topology)Boundary value problemInverseState (computer science)Mathematical analysisFixed-point iterationIterative methodScheme (mathematics)Point (geometry)Mathematical optimizationState variableNoisy dataFinite element methodVariable (mathematics)Initial value problemInverse systemGeneralized inverseFinite setNumerical methods in inverse problemsElectrical and Bioimpedance TomographyMicrowave Imaging and Scattering Analysis