On the Recovery of Surface Temperature and Heat Flux via Convolutions

  • B. A. Mair
Part of the Progress in Systems and Control Theory book series (PSCT, volume 1)


The determination of the surface temperature and heat flux of a body by means of interior temperature measurements is very important in many areas of science and industry (cf. [1], [8], [9]), and is usually referred to as inverse heat conduction problems (IHCP). Due to their wide applicability, much emphasis has been placed on the numerical solutions of these IHCP. It is stated in [1] that few exact (or, analytic) solutions have been found, and that the known exact soluti ons usually have quite restrictive assumptions imposed on the boundary data (such as infinite differentiability).


Heat Flux Boundary Data Noisy Data Tikhonov Regularization Inversion Scheme 
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]
    J. V. BECK, B. BLACKWELL, C. R. St. CLAIR, Jr., Inverse Heat Conduction: Ill-Posed Problems, Wiley, 1985.Google Scholar
  2. [2]
    G. BIRKHOFF, G-C. ROTA, Ordinary Differential Equations, Blais-dell Pub. Co., 1969.Google Scholar
  3. [3]
    A. Carasso, “Determining surface temperatures from interior observations”, SIAM J. Appl. Math., 42, No. 3, (1982), 558–574.MathSciNetzbMATHCrossRefGoogle Scholar
  4. [4]
    D.S. Gilliam, B. A. Mair, “Stability of a convolution method for inverse heat conduction problems”, submitted.Google Scholar
  5. [5]
    D. S. Gilliam, B. A. Mair, C. F. Martin, “A convolution method for inverse heat conduction problems”, Math. Systems Theory, 21, (1988), 49–60.MathSciNetzbMATHCrossRefGoogle Scholar
  6. [6]
    D. S. Gilliam, “An inverse convolution method for regular parabolic equations”, submitted.Google Scholar
  7. 7.
    E. HILLE, Lectures on Ordinary Differential Equations, Addison-Wesley Pub. Co., 1969.Google Scholar
  8. [8]
    V. A. MOZOROV, Methods for Solving Incorrectly Posed Problems, Springer-Verlag, 1984.Google Scholar
  9. [9]
    L. E. PAYNE, Improperly Posed Problems in Partial Differential Equations, CBMS Regional Conference Series, 22, SIAM, Philadelphia, 1975.Google Scholar
  10. [10]
    A. N. Tikhonov, V. Y. ARSENIN, Solutions of Ill-Posed Problems, Wiley, 1977.Google Scholar
  11. [11]
    A. N. Tikhonov, V. V. Glasko, “Methods of determining the surface temperature in a body”, USSR Comp. Math, and Math. Phys. 7, (1967), 267–273.CrossRefGoogle Scholar
  12. [12]
    C. R. Vogel, “Optimal choice of a truncation level for the truncated SVD solution of linear first kind integral equations when data are noisy”, SIAM J. Numer. Anal, 23, No. 1 (1986), 109–117.MathSciNetzbMATHCrossRefGoogle Scholar
  13. [13]
    E. ZAUDERER, Partial Differential Equations of Applied Mathematics, Wiley-Interscience, 1983.Google Scholar

Copyright information

© Birkhäuser Boston 1989

Authors and Affiliations

  • B. A. Mair
    • 1
  1. 1.Department of MathematicsTexas Tech UniversityLubbockUSA

Personalised recommendations