Chein-Shan Liu^{1}, Chih-Wen Chang^{2}

*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 *T*_{t}(x, t) = *T*_{xx}(x, t)-*α(x)T(x, t)*, and *T*_{t}(x, y, t) = *T*_{xx}(x, y, t) + *T*_{yy}(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 >