Identification of the Right-Hand Side of an Equation with a Fractional Power of an Elliptic Operator

  • Petr N. VabishchevichEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11189)


An inverse problem of identifying the right-hand side of an equation with a fractional power of an elliptic operator by the solution is considered. The direct problem is solved via solving a Cauchy problem for a pseudo-parabolic equation. The problem of identifying the right-hand side is reduced to a retrospective problem for this pseudo-parabolic equation. An iterative method is employed to adjust the initial condition. The results of numerical experiments for a 2D inverse problem are presented.


Fractional power of an elliptic operator Identification of the right-hand side Retrospective inverse problem Iterative method for solving an ill-posed problem 


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Nuclear Safety InstituteRussian Academy of SciencesMoscowRussia
  2. 2.Akhmet Yasawi International Kazakh-Turkish UniversityTurkistanKazakhstan

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