Identification of Heat Conductivity in (2+1)D Equation as a Function of Time

  • Tchavdar T. Marinov
  • Rossitza S. MarinovaEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11958)


The considered problem for identifying the time–dependent heat conductivity coefficient from over–posed boundary data belongs to a class of inverse problems. The proposed solution uses a variational approach for identifying the coefficient. The inverse problem is reformulated as a higher–order elliptic boundary–value problem for minimization of a quadratic functional of the original equation. The resulting system consists of a well–posed fourth–order boundary-value problem for the temperature and an explicit equation for the unknown heat conductivity coefficient. The obtained boundary–value problem is solved by means of an iterative procedure, which is thoroughly validated.


Heat conductivity Inverse problem Variational method Boundary data 


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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Southern University at New OrleansNew OrleansUSA
  2. 2.Concordia University of EdmontonEdmontonCanada

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