On the Recovery of Surface Temperature and Heat Flux via Convolutions
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. , , ), 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  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).
KeywordsHeat Flux Boundary Data Noisy Data Tikhonov Regularization Inversion Scheme
Unable to display preview. Download preview PDF.
- J. V. BECK, B. BLACKWELL, C. R. St. CLAIR, Jr., Inverse Heat Conduction: Ill-Posed Problems, Wiley, 1985.Google Scholar
- G. BIRKHOFF, G-C. ROTA, Ordinary Differential Equations, Blais-dell Pub. Co., 1969.Google Scholar
- D.S. Gilliam, B. A. Mair, “Stability of a convolution method for inverse heat conduction problems”, submitted.Google Scholar
- D. S. Gilliam, “An inverse convolution method for regular parabolic equations”, submitted.Google Scholar
- 7.E. HILLE, Lectures on Ordinary Differential Equations, Addison-Wesley Pub. Co., 1969.Google Scholar
- V. A. MOZOROV, Methods for Solving Incorrectly Posed Problems, Springer-Verlag, 1984.Google Scholar
- L. E. PAYNE, Improperly Posed Problems in Partial Differential Equations, CBMS Regional Conference Series, 22, SIAM, Philadelphia, 1975.Google Scholar
- A. N. Tikhonov, V. Y. ARSENIN, Solutions of Ill-Posed Problems, Wiley, 1977.Google Scholar
- E. ZAUDERER, Partial Differential Equations of Applied Mathematics, Wiley-Interscience, 1983.Google Scholar