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Fractal diffusion retrospective problems

Year 2014, Volume: 2 Issue: 3, 9 - 14, 08.10.2014

Oleg Yaremko

https://doi.org/10.18100/ijamec.31655

Abstract

In this article we study the retrospective inverse problem. The retrospective inverse problem consists of in the reconstruction of a priori unknown initial condition of the dynamic system from its known final condition. Existence and uniqueness of the solution is proved.

Keywords

Hermite functions retrospective problem integral equation fractal diffusion.

References

  • F.M. Mors, G. Fishbah, Methods of theoretical physics, 1958.
  • Yaremko, O.E. Matrix integral Fourier transforms for problems with discontinuous coefficients and transformation operators (2007) Doklady Mathematics, 76 (3), pp. 323-325.
  • O.M. Alifanov, Inverse problems of heat exchange, M, 1988, p. 279.
  • O.M. Alifanov, B.A. Artyukhin, S.V. Rumyancev, The extreme methods of solution of ill-posed problems, M, 1988, p. 288.
  • J.V. Beck, V. Blackwell, C.R. Clair, Inverse Heat Conduction. Ill-Posed Problems , M, 1989, p. 312.
  • V.K. Ivanov, V.V. Vasin, V.P. Tanana, Theory of linear ill-posed problems and its applications, M, 1978, p. 206.
  • M.M. Lavrentev, Some ill-posed problems of mathematical physics, Novosibirsk, AN SSSR,1962, p. 92.
  • A.N. Tikhonov, V. Ya. Arsenin, Methods of solution of ill-posed problems, M,1979, p. 288.
  • .
  • M.M. Dzhrbashyan, Integral Transforms and Representations of Functions in the Complex Domain, M, 1966.

Original Research Paper

Year 2014, Volume: 2 Issue: 3, 9 - 14, 08.10.2014

Oleg Yaremko

https://doi.org/10.18100/ijamec.31655

Abstract

References

  • F.M. Mors, G. Fishbah, Methods of theoretical physics, 1958.
  • Yaremko, O.E. Matrix integral Fourier transforms for problems with discontinuous coefficients and transformation operators (2007) Doklady Mathematics, 76 (3), pp. 323-325.
  • O.M. Alifanov, Inverse problems of heat exchange, M, 1988, p. 279.
  • O.M. Alifanov, B.A. Artyukhin, S.V. Rumyancev, The extreme methods of solution of ill-posed problems, M, 1988, p. 288.
  • J.V. Beck, V. Blackwell, C.R. Clair, Inverse Heat Conduction. Ill-Posed Problems , M, 1989, p. 312.
  • V.K. Ivanov, V.V. Vasin, V.P. Tanana, Theory of linear ill-posed problems and its applications, M, 1978, p. 206.
  • M.M. Lavrentev, Some ill-posed problems of mathematical physics, Novosibirsk, AN SSSR,1962, p. 92.
  • A.N. Tikhonov, V. Ya. Arsenin, Methods of solution of ill-posed problems, M,1979, p. 288.
  • .
  • M.M. Dzhrbashyan, Integral Transforms and Representations of Functions in the Complex Domain, M, 1966.
There are 10 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Oleg Yaremko

Publication Date October 8, 2014
Published in Issue Year 2014 Volume: 2 Issue: 3

Cite

APA Yaremko, O. (2014). Fractal diffusion retrospective problems. International Journal of Applied Mathematics Electronics and Computers, 2(3), 9-14. https://doi.org/10.18100/ijamec.31655
AMA Yaremko O. Fractal diffusion retrospective problems. International Journal of Applied Mathematics Electronics and Computers. October 2014;2(3):9-14. doi:10.18100/ijamec.31655
Chicago Yaremko, Oleg. “Fractal Diffusion Retrospective Problems”. International Journal of Applied Mathematics Electronics and Computers 2, no. 3 (October 2014): 9-14. https://doi.org/10.18100/ijamec.31655.
EndNote Yaremko O (October 1, 2014) Fractal diffusion retrospective problems. International Journal of Applied Mathematics Electronics and Computers 2 3 9–14.
IEEE O. Yaremko, “Fractal diffusion retrospective problems”, International Journal of Applied Mathematics Electronics and Computers, vol. 2, no. 3, pp. 9–14, 2014, doi: 10.18100/ijamec.31655.
ISNAD Yaremko, Oleg. “Fractal Diffusion Retrospective Problems”. International Journal of Applied Mathematics Electronics and Computers 2/3 (October 2014), 9-14. https://doi.org/10.18100/ijamec.31655.
JAMA Yaremko O. Fractal diffusion retrospective problems. International Journal of Applied Mathematics Electronics and Computers. 2014;2:9–14.
MLA Yaremko, Oleg. “Fractal Diffusion Retrospective Problems”. International Journal of Applied Mathematics Electronics and Computers, vol. 2, no. 3, 2014, pp. 9-14, doi:10.18100/ijamec.31655.
Vancouver Yaremko O. Fractal diffusion retrospective problems. International Journal of Applied Mathematics Electronics and Computers. 2014;2(3):9-14.
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