About one approach to solving the inverse problem for parabolic equation

Aleksei P. Zhabko, Karlygash B. Nurtazina, Vyacheslav V. Provotorov

Research output: Contribution to journalArticlepeer-review

16 Scopus citations


Consider the problem of determining the coefficients in the differential equation of parabolic types and boundary conditions on the known sections of the solutions of the initial-boundary value problem. Used spectral approach based on spectral properties of the elliptic operator of the initial-boundary value problem and the methods of solving the inverse spectral problem of restoring the Sturm-Liouville operator on two sequences of the eigenvalues, that corresponding to two sets of boundary conditions. In the work presented sufficient conditions of determination of two sequences of the eigenvalues by two sets of boundary conditions and terms of the uniqueness of the solution of the inverse problem The paper considers the case where the initial-boundary value problem contains the specifics - the interval of change contains variable include a finite number of the points, where the differential equation is meaningless and replaced conditions agreement.

Original languageEnglish
Pages (from-to)323-336
Number of pages14
JournalVestnik Sankt-Peterburgskogo Universiteta, Prikladnaya Matematika, Informatika, Protsessy Upravleniya
Issue number3
StatePublished - 1 Jan 2019

Scopus subject areas

  • Computer Science(all)
  • Control and Optimization
  • Applied Mathematics


  • Inverse problem
  • Parabolic system
  • The eigenvalues of boundary value problems
  • The poles of the analytical continuation of the Green's function


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