Identification of nonlinear heat transfer laws from boundary observations
- 14 August 2014
- journal article
- research article
- Published by Taylor & Francis Ltd in Applicable Analysis
- Vol. 94 (9), 1784-1799
- https://doi.org/10.1080/00036811.2014.948425
Abstract
We consider the problem of identifying a nonlinear heat transfer law at the boundary, or of the temperature-dependent heat transfer coefficient in a parabolic equation from boundary observations. As a practical example, this model applies to the heat transfer coefficient that describes the intensity of heat exchange between a hot wire and the cooling water in which it is placed. We reformulate the inverse problem as a variational one which aims to minimize a misfit functional and prove that it has a solution. We provide a gradient formula for the misfit functional and then use some iterative methods for solving the variational problem. Thorough investigations are made with respect to several initial guesses and amounts of noise in the input data. Numerical results show that the methods are robust, stable and accurate.Keywords
This publication has 21 references indexed in Scilit:
- Determination of the heat transfer coefficients in transient heat conductionInverse Problems, 2013
- Recovering temperature dependence of heat transfer coefficient in electronic circuitsInverse Problems in Science and Engineering, 2009
- Natural linearization for the identification of nonlinear heat transfer lawsJIIP, 2005
- On the determination of an unknown boundary function in a parabolic equationInverse Problems, 1999
- Pontryagin's Principle for State-Constrained Boundary Control Problems of Semilinear Parabolic EquationsSIAM Journal on Control and Optimization, 1997
- Stability estimates for the identification of nonlinear heat transfer lawsInverse Problems, 1996
- Fréchet Differentiability of the Solution of the Heat Equation with Respect to a Nonlinear Boundary ConditionZeitschrift für Analysis und ihre Anwendungen, 1996
- Identification of nonlinear heat transfer laws by optimal controlNumerical Functional Analysis and Optimization, 1994
- Boundary control for the heat equation with non-linear boundary conditionJournal of Differential Equations, 1989
- An iteration method for the determination of an unknown boundary condition in a parabolic initial-boundary value problemProceedings of the Edinburgh Mathematical Society, 1989