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arXiv · 1311.4442

On a new formulas for a direct and inverse Cauchy problems of heat equation

N. Yaremko·O. Yaremko
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Abstract

In this paper a solution of the direct Cauchy problems for heat equation is founded in the Hermite polynomial series form. A well-known classical solution of direct problem is represented in the Poisson integral form. The author shows the formulas for the solution of the inverse Cauchy problems have a symmetry with respect to the formulas for the corresponding direct problems. The obtained solution formulas for the inverse problems can serve as a basis for regularizing computational algorithms while well-known classical formula for the solution of inverse problem did not possess such properties and can't be a basis for regularizing computational algorithms.

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N. Yaremko, O. Yaremko. 2013-11-18. On a new formulas for a direct and inverse Cauchy problems of heat equation. https://arxiv.org/abs/1311.4442

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