Inverse problems for diffusion operator with discontinuity function


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Ergün A.

ISMS-International Symposium on Multidisciplinary Studies, Paris, France, 26 - 27 June 2018, pp.3-4

  • Publication Type: Conference Paper / Summary Text
  • City: Paris
  • Country: France
  • Page Numbers: pp.3-4

Abstract

In this study, diffusion operator with discontinuity function is considered. In the beginning, integral

equations for solving the given initial conditions of the given problem are obtained, integral

representations of the solutions which are very useful for the diffusion equation are obtained and the

important features of the eigenvalues and eigenfunctions of the problem are found by using these

representations. Using the obtained equations and asymptotic expressions, it has been proved that the

coefficients of the diffusion operator with discontinuity function can be determined with the help of

Weyl function, and it has been proved that the operator can be uniquely determined with the help of

spectral data.