Continuous dependence of solutions of inverse boundary value problems in one-dimensional heat conduction
DOI:
https://doi.org/10.22199/S07160917.1992.0002.00005Keywords:
Ill-posed problems, Inverse heat conductionAbstract
Results on uniqueness and continuous dependence upon the internal data of the solutions to some inverse boundary problems of heat conduction in one spatial dimension are given under some smoothness conditions.
References
[ 1] Beck, J. V.; Blackwell, B. & Clair, C. R.: lnverse Heat Conduction -Ill- Posed Problems, Wiley, 1985.
[ 2] Cannon, J.R.: The One-Dimensional Heat Equation, Encyclopedia Math. Appl. 23, Addison Wesley, 1984.
[ 3] Cannon, J.R. and Esteva, S.P.: An inverse problem for the heat equation, Inv. Problems, 2, pp. 395-403, 1987.
[ 4] Grysa. K.: On the exact and approximate methods of solving the inverse problems of temperature fields, Rozprawy Politech. Poznan. 204, 1989 (in Polish).
[ 5] Hensel, E.C.& Hills, R.G.: An initial value approach to the inverse heat conduction problem, ASME J. Heat Transfer, (2) 108, pp.248-256, 1986.
[ 6] Manselli, P. & Miller, K.: Calculation of the surface temperature and the heat flux on one side of a wall from measurements on the opposite side, Ann. Mat. Pura Appl., , (4) 123, pp.161-183, 1980.
[ 7] Muria, D.A.: Parameter selection by discrete modification and the numerical solution of the inverse heat conduction problem, J. Comp. Appl. Math., 22, pp. 25-34, 1988.
[ 8] Stolz, G.: Numerical solution to an inverse problem of heat conduction for simple shapes, J. Heat Transfer, 82, pp.20-26, 1960.
[ 9] Weber, C.: Analysis and solution of the ill-posed inverse heat conduction problem, Internat J. Heat Mass Trans., 24, pp. 1783-1792, 1981.
[10] Widder, D. V.: The Heat Equation, Academic Press, New York, 1975.
[ 2] Cannon, J.R.: The One-Dimensional Heat Equation, Encyclopedia Math. Appl. 23, Addison Wesley, 1984.
[ 3] Cannon, J.R. and Esteva, S.P.: An inverse problem for the heat equation, Inv. Problems, 2, pp. 395-403, 1987.
[ 4] Grysa. K.: On the exact and approximate methods of solving the inverse problems of temperature fields, Rozprawy Politech. Poznan. 204, 1989 (in Polish).
[ 5] Hensel, E.C.& Hills, R.G.: An initial value approach to the inverse heat conduction problem, ASME J. Heat Transfer, (2) 108, pp.248-256, 1986.
[ 6] Manselli, P. & Miller, K.: Calculation of the surface temperature and the heat flux on one side of a wall from measurements on the opposite side, Ann. Mat. Pura Appl., , (4) 123, pp.161-183, 1980.
[ 7] Muria, D.A.: Parameter selection by discrete modification and the numerical solution of the inverse heat conduction problem, J. Comp. Appl. Math., 22, pp. 25-34, 1988.
[ 8] Stolz, G.: Numerical solution to an inverse problem of heat conduction for simple shapes, J. Heat Transfer, 82, pp.20-26, 1960.
[ 9] Weber, C.: Analysis and solution of the ill-posed inverse heat conduction problem, Internat J. Heat Mass Trans., 24, pp. 1783-1792, 1981.
[10] Widder, D. V.: The Heat Equation, Academic Press, New York, 1975.
Published
2018-04-02
How to Cite
[1]
W. Golik L., “Continuous dependence of solutions of inverse boundary value problems in one-dimensional heat conduction”, Proyecciones (Antofagasta, On line), vol. 11, no. 2, pp. 131-142, Apr. 2018.
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