On an optimal method for solving an inverse Stefan problem

  • V. P. Tanana
  • E. V. Khudyshkina


An algorithm optimal in order is proposed for solving an inverse Stefan problem. We also give some exact estimates of accuracy of this method.


Initial Problem Stefan Problem Exact Estimate Transition Front Isometric Operator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    N. L. Gol’dman, Inverse Stefan Problems: Theory and Solution Methods (MGU, Moscow, 1999) [in Russian].Google Scholar
  2. 2.
    A. Friedman, Partial Differential Equations of Parabolic Type (Prentice-Hall, Englewood Cliffs, N.J., 1964; Mir, Moscow, 1968).MATHGoogle Scholar
  3. 3.
    O. M. Alifanov, E. A. Artyukhin, and S. V. Rumyantsev, Optimal Methods for Solving the Ill-Posed Problems (Nauka, Moscow, 1988) [in Russian].Google Scholar
  4. 4.
    M. M. Lavrent’ev and L. Ya. Savel’ev, Theory of Operators and Ill-Posed Problems (Sobolev Inst. Mat., Novosibirsk, 1999) [in Russian].MATHGoogle Scholar
  5. 5.
    V. P. Tanana, “On Optimality by Order of the Method of Projective Regularization for Solving Inverse Problems,” Sibirsk. Zh. Industr. Mat. 7(2), 117–132 (2004).MATHMathSciNetGoogle Scholar
  6. 6.
    V. A. Ditkin and A. P. Prudnikov, Integral Transformations and Operational Calculus (Nauka, Moscow, 1961) [in Russian].Google Scholar
  7. 7.
    L. D. Menikhes and V. P. Tanana, “Finite-Dimensional Approximation in the M. M. Lavrent’ev Method,” Sibirsk. Zh. Vychisl. Mat. 1(1), 59–66 (1998).MathSciNetGoogle Scholar
  8. 8.
    V. K. Ivanov and T. I. Korolyuk, “On an Error Estimate for Solution of Linear Ill-Posed Problems,” Zh. Vychisl. Mat. i Mat. Fiz. 9(1), 30–41 (1969).MATHGoogle Scholar
  9. 9.
    V. N. Strakhov, “Solution of Linear Ill-Posed Problems in Hilbert Space,” Differentsial’nye Uravneniya 6(8), 1490–1495 (1970).MATHGoogle Scholar
  10. 10.
    V. K. Ivanov, V. V. Vasin, and V. P. Tanana, Theory of Ill-Posed Linear Problems and Its Applications (Nauka, Moscow, 1978) [in Russian].MATHGoogle Scholar
  11. 11.
    V. P. Tanana, “On a New Approach to the Error Estimate of the Methods for Solving Ill-Posed Problems,” Sibirsk. Zh. Industr. Mat. 5(4), 150–163 (2002).MATHMathSciNetGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2007

Authors and Affiliations

  • V. P. Tanana
    • 1
  • E. V. Khudyshkina
    • 1
  1. 1.Chelyabinsk State UniversityChelyabinskRussia

Personalised recommendations