Examples of incorrectly posed inverse problems
Inverse problems in heat diffusion . Construction and solution of the least squares problem

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Examples of incorrectly posed inverse problems


Inverse problems in heat diffusion . Construction and solution of the least squares problem

Authors : Denis MAILLET, Yvon JARNY, Daniel PETIT

Publication date: July 10, 2018 | Lire en français

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4. Examples of incorrectly posed inverse problems

4.1 A simple case of inversion: stationary 1D conduction in a plane wall. Example 1

Here we consider the problem of permanent unidirectional heat transfer in a homogeneous wall. We know the exact temperature T e on the face x = e and we measure the temperature y from a sensor implanted at a depth x c in the medium. Using these two pieces of information and knowing the exact values of the conductivity λ and the thickness e of the wall, we seek to estimate (figure 6 a ) :

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