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A nonstandard Cauchy problem for the heat equation

Abstract

We consider the Cauchy problem for the heat equation in a cylinder C T = X × (0, T) over a domain X in Rn, with data on a strip lying on the lateral surface. The strip is of the form S × (0, T), where S is an open subset of the boundary of X. The problem is ill-posed. Under natural restrictions on the configuration of S, we derive an explicit formula for solutions of this problem.

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Correspondence to K. O. Makhmudov.

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Original Russian Text © K. O. Makhmudov, O. I. Makhmudov, N. Tarkhanov, 2017, published in Matematicheskie Zametki, 2017, Vol. 102, No. 2, pp. 270–283.

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Makhmudov, K.O., Makhmudov, O.I. & Tarkhanov, N. A nonstandard Cauchy problem for the heat equation. Math Notes 102, 250–260 (2017). https://doi.org/10.1134/S0001434617070264

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  • DOI: https://doi.org/10.1134/S0001434617070264