A Lie-Group Adaptive Method to Identify the Radiative Coefficients in Parabolic Partial Differential Equations
Chein-Shan Liu1, Chih-Wen Chang2
CMC-Computers, Materials & Continua, Vol.25, No.2, pp. 107-134, 2011, DOI:10.3970/cmc.2011.025.107
Abstract We consider two inverse problems for estimating radiative coefficients α(x) and α(x, y), respectively, in Tt(x, t) = Txx(x, t)-α(x)T(x, t), and Tt(x, y, t) = Txx(x, y, t) + Tyy(x, y, t)-α(x, y)T(x, y, t), where a are assumed to be continuous functions of space variables. A Lie-group adaptive method is developed, which can be used to find a at the spatially discretized points, where we only utilize the initial condition and boundary conditions, such as those for a typical direct problem. This point is quite different from other methods, which need the overspecified final time data. Three-fold advantages can be gained More >
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