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

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

2008-10-09

arxiv.org/abs/0810.1561v1

Inverse Problems 25(2009) 035011(21pp)

Mathematics

Analysis of PDEs

1 figure, 26pages

Scientific paper

10.1088/0266-5611/25/3/035011

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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