Identification of Heat Conductivity in (2+1)D Equation as a Function of Time
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The considered problem for identifying the time–dependent heat conductivity coefficient from over–posed boundary data belongs to a class of inverse problems. The proposed solution uses a variational approach for identifying the coefficient. The inverse problem is reformulated as a higher–order elliptic boundary–value problem for minimization of a quadratic functional of the original equation. The resulting system consists of a well–posed fourth–order boundary-value problem for the temperature and an explicit equation for the unknown heat conductivity coefficient. The obtained boundary–value problem is solved by means of an iterative procedure, which is thoroughly validated.
KeywordsHeat conductivity Inverse problem Variational method Boundary data
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