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A modified method for determining the surface heat flux of IHCP. (English) Zbl 1202.80017
Summary: We consider the determination of the surface heat flux of a body from a measured temperature history at a fixed location inside the body. Mathematically, it is formulated as a problem for the one-dimensional heat equation in a quarter plane with data given along the line $$x = 1$$, and the gradient of the solution is determined for $$0\leq x < 1$$. This problem is of practical interest in some engineering contexts and it is severely ill-posed, in the sense that the solution (if it exists) does not depend continuously on the data. In this article, we employ a fourth-order modified method to solve the problem. Some stability estimates are given. Numerical examples show that the modified method works very well.

MSC:
 80A23 Inverse problems in thermodynamics and heat transfer 80A20 Heat and mass transfer, heat flow (MSC2010) 35R30 Inverse problems for PDEs
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References:
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