The source control in the problem of heat conduction

Authors

  • V.A. Morozov
  • N.M. Tokarev
  • V.G. Lezhnev

Keywords:

heat conduction
boundary value problems
inverse problem of heat conduction
control of distributed parameters

Abstract

For the heat conduction equation, a boundary value problem that consists in determining the density of volume sources which provides a prescribed final (T > 0) temperature distribution is considered. The correctness of the problem is proved, a convergent algorithm is constructed, and an algorithm for solving the inverse problem of heat conduction is proposed. The work was performed in the framework of the target program (project 2.1.1/1292) and was supported by the Russian Foundation for Basic Research (projects 11–01–96511a and 13–01–00096a).

New computational technologies

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Published

2013-02-17

Issue

Vol. 14 (2013): Issue 1.

Section

Section 1. Numerical methods and applications

Author Biographies

V.A. Morozov

Lomonosov Moscow State University,
Research Computing Center
• Chief Researcher

N.M. Tokarev

Kuban State University,
Faculty of Mathematics and Computer Sciences
• Lecturer

V.G. Lezhnev

Kuban State University,
Faculty of Mathematics and Computer Sciences
• Professor

References

  1. Алифанов О.М. Обратные задачи теплообмена. М.: Машиностроение, 1988.
  2. Лежнев В.Г., Марковский А.Н. К решению обратной задачи теплопроводности // Сибирские электронные математические известия.
  3. Михайлов В.П. Дифференциальные уравнения в частных производных. М.: Наука, 1983.
  4. Морозов В.А. Регулярные методы решения некорректно поставленных задач. М.: Изд-во Моск. ун-та, 1987.
  5. Морозов В.А., Лежнев В.Г., Токарев Н.М. Вариационная задача для бигармонического уравнения // Вычислительные методы и программирование. 2012. 13, № 2. 409-412.