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arXiv · 0810.1561

Two analytical formulae of the temperature inside a body by using partial lateral and initial data

Masaru Ikehata
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Abstract

This paper considerers the problem of computing the value of a solution of the heat equation at a given point inside a bounded domain after the initial time. It is assumed that the initial value of the solution inside the domain (possibly in a part of the domain) is known; the boundary value and the normal derivative on a part of the boundary of the domain over a finite time interval are known. Two analytical formulae for the problem are given. Both formulae make use of a special fundamental solution having a large parameter of the backward heat equation.

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Masaru Ikehata. 2008-10-09. Two analytical formulae of the temperature inside a body by using partial lateral and initial data. https://doi.org/10.1088/0266-5611%2F25%2F3%2F035011

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