Determination of a time-dependent thermal diffusivity and free boundary in heat conduction
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Publication Date
Fri Jan 01 2016
Journal Name
Applied Numerical Mathematics
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Publication Date
Sat Aug 24 2024
Journal Name
Mathematics
Identification of Time-Wise Thermal Diffusivity, Advection Velocity on the Free-Boundary Inverse Coefficient Problem
This paper is concerned with finding solutions to free-boundary inverse coefficient problems. Mathematically, we handle a one-dimensional non-homogeneous heat equation subject to initial and boundary conditions as well as non-localized integral observations of zeroth and first-order heat momentum. The direct problem is solved for the temperature distribution and the non-localized integral measurements using the Crank–Nicolson finite difference method. The inverse problem is solved by simultaneously finding the temperature distribution, the time-dependent free-boundary function indicating the location of the moving interface, and the time-wise thermal diffusivity or advection velocities. We reformulate the inverse problem as a non-
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Publication Date
Thu Jan 01 2015
Journal Name
Finite Difference Methods,theory And Applications
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Publication Date
Tue Mar 16 2021
Journal Name
International Journal For Computational Methods In Engineering Science And Mechanics
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Publication Date
Thu Jun 01 2023
Journal Name
Partial Differential Equations In Applied Mathematics
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Publication Date
Fri Oct 14 2016
Journal Name
International Journal For Computational Methods In Engineering Science And Mechanics
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Publication Date
Sat Mar 01 2014
Journal Name
Computers & Mathematics With Applications
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Publication Date
Fri Nov 01 2013
Journal Name
East Asian Journal On Applied Mathematics
Free Boundary Determination in Nonlinear Diffusion
Abstract<p>Free boundary problems with nonlinear diffusion occur in various applications, such as solidification over a mould with dissimilar nonlinear thermal properties and saturated or unsaturated absorption in the soil beneath a pond. In this article, we consider a novel inverse problem where a free boundary is determined from the mass/energy specification in a well-posed one-dimensional nonlinear diffusion problem, and a stability estimate is established. The problem is recast as a nonlinear least-squares minimisation problem, which is solved numerically using the <italic>lsqnonlin</italic> routine from the MATLAB toolbox. Accurate and stable numerical solutions are achieved. For noisy data, inst</p>
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Publication Date
Thu Feb 01 2018
Journal Name
Applied Mathematical Modelling
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Publication Date
Fri Apr 01 2016
Journal Name
Communications In Nonlinear Science And Numerical Simulation
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