Recovering A Heat Source and Initial Value by a Lie-Group Differential Algebraic Equations Method |
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Authors: | Chein-Shan Liu Chung-Lun Kuo |
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Affiliation: | 1. Department of Civil Engineering , National Taiwan University , Taipei , Taiwan , Republic of China;2. Department of Systems Engineering and Naval Architecture , National Taiwan Ocean University , Keelung , Taiwan , Republic of China |
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Abstract: | We consider an inverse problem of a nonlinear heat conduction equation for recovering unknown space-dependent heat source and initial condition under Cauchy-type boundary conditions, which is known as a sideways heat equation. With the aid of two extra measurements of temperature and heat flux which are being polluted by noisy disturbances, we can develop a Lie-group differential algebraic equations (LGDAE) method to solve the resulting differential algebraic equations, and to quickly recover the unknown heat source and initial condition simultaneously. Also, we provide a simple LGDAE method, without needing extra measurement of heat flux, to recover the above two unknown functions. The estimated results are quite promising and robust enough against large random noise. |
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