Abstract
The paper deals with the possibility to solve the heat equation backwards in time. More specifically, we treat the following problem. Given the temperature at a finite number of points of a homogeneous bar, how old can the heat distribution be? In the case that the temperature is given at equidistant points x1, the problem is completely solved. In the case of nonequidistant xi we find an upper bound for the age. Such a bound is also obtained when the information about the heat distribution is given by the value of a finite number of linear functionals.
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References
Krein, M. G., The ideas of P. L. Chebyshev and A. A. Markov in the theory of limiting values of integrals and their further developmentAmer. Math. Soc. Translations, ser. 2, no. 12, 3–120 (1951).
Rogosinski, W. W., Moments of non-negative mass,Proc. Roy. Soc. (London) A,245, 1–27 (1958).
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Philip, J. Estimates of the age of a heat distribution. Ark. Mat. 7, 351–358 (1968). https://doi.org/10.1007/BF02591028
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DOI: https://doi.org/10.1007/BF02591028