On Reducing an Inverse Boundary-Value Problem to the Synthesis of Two Ill-Posed Problems and Their Solution

ABSTRACT

An inverse boundary-value problem for the heat conduction equation is solved, and the error of the approximate solution is estimated. The Fourier transform with respect to time, which allows one to obtain an error estimate, is not applicable to the problem to be solved. Therefore, the variable in the heat conduction equation is replaced, resulting in the synthesis of problems and obtaining the estimate.

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Tanana, V.P. On Reducing an Inverse Boundary-Value Problem to the Synthesis of Two Ill-Posed Problems and Their Solution. Numer. Analys. Appl. 13, 180–192 (2020). https://doi.org/10.1134/S1995423920020081

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Keywords

  • error estimate
  • modulus of continuity
  • Fourier transform
  • ill-posed problem