Skip to main content
SpringerLink
Log in

Reverse problems for diffusion equation

Inverse Randwertprobleme der diffusion

  • Published:
Archiv für Elektrotechnik Aims and scope Submit manuscript

Contents

The paper deals with the analysis of the reverse problems for diffusion equation depending on determination of the boundary conditions of the first and second kind. The idea of proposed method consists on solving the Volterra integral equations of the first kind by means of Tichonov's regularisation method. Theoretical consideration were illustrated by numerical calculations of reverse problems for the uniformR, C transmission line.

Übersicht

Im Rahmen der vorliegenden Abhandlung werden dic Randbedingungen erster und zweiter Art von inversen Diffusionsrandwertproblemen bestimmt. Den Ausganspunkt der Überlegungen bildet die Regularisationsmethode von Tichonov zur Lösung der Volterra-Integralgleichung erster Art. Die theoretischen Ergebnisse werden am Beispiel einerRC-Ubertrangnngsstrecke numerisch ausgewertet.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Butkowski, A. G.: Control of distributed parameters systems. Moscow: Nauka, 1975

    Google Scholar 

  2. Fox, L.: Numerical solution of ordinary and partial differential equations, London: Oxford, 1962

    Google Scholar 

  3. Friedman, A.: Optimal control for parabolic equations. J. Math. Anal. and Appl. 18/3, (1967)

  4. Hanson, R. J.; Phillips, J. L.: An adaptive method for solving linear Fredholm integral equation of the first kind. Num. Mat. 24/4, (1975)

  5. Lattes, R.; Lions, J.-L.: Methode de quasi-réversibilite et applications. Paris 1967

  6. Lewis, B. A.: On the Numerical Solution of Fredholm Integral Equations of the First Kind. J. Inst. Math. Applics. 16/2 (1975)

  7. Lions, J.-L.: Controle optimal de sysétmes gouvernes par des équations aux dérivees partielles. Paris 1968

  8. McCamy, R. C.; Mizel, V. J.; Seidman, T. J.: Approximate boundary controllability for the heat equation. J. Math. Anal, and Appl. 28/3 (1969)

  9. Miranker, W. L.: Approximate controllability for distributed linear systems. J. Math. Anal. and Appl. 10/2 (1965)

  10. Mizel, V. J.; Seidman, T. J.: Observation and prediction for the heat equation. J. Math. Anal. and Appl 28/2 (1969)

    Google Scholar 

  11. Paŀka, R.; Sikora, R.: Reverse Problem of Diffusion of Electromagnetic Field into Conducting Region. INTERMAG 1978. IEEE Magnetics, Sept. 1978

  12. Sikora, R.; Purczyński, J.; Adamiak, K.: The Magnetic Field Synthesis on a Cylinder Solenoid Axis by Means of Tichonov's Regularisation Method. Arch. f. Elektrotech. 60 (1978) 83–86

    Google Scholar 

  13. Tichonov, A. N., Arsjenin, W. Ja.: Methods of solving ill posed problems. Moscow: Nauka, 1974.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. 6/4 Podhalaŝka St., 70-452, Szczecin, Poland

    R. Sikora

  2. 5A Jagodowa St., Szczecin, Poland

    R. Palka

Authors
  1. R. Sikora
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. R. Palka
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sikora, R., Palka, R. Reverse problems for diffusion equation. Archiv f. Elektrotechnik 62, 177–180 (1980). https://doi.org/10.1007/BF01579902

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01579902

Keywords

Search

Navigation