Determination of One Unknown Thermal Coefficient through the One-Phase Fractional Lamé-Clapeyron-Stefan Problem

作     者：Domingo Alberto Tarzia 

作者机构：CONICET and Department of Mathematics FCE Universidad Austral Rosario Argentina 

出 版 物：《Applied Mathematics》 (应用数学（英文）)

年 卷 期：2015年第6卷第13期

页      面：2182-2191页

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

主　　题：Free Boundary Problems Fractional Diffusion Lamé-Clapeyron-Stefan Problem Unknown Thermal Coefficients Explicit Solution Over-Specified Boundary Condition 

摘      要：We obtain explicit expressions for one unknown thermal coefficient (among the conductivity, mass density, specific heat and latent heat of fusion) of a semi-infinite material through the one-phase fractional Lamé-Clapeyron-Stefan problem with an over-specified boundary condition on the fixed face . The partial differential equation and one of the conditions on the free boundary include a time Caputo’s fractional derivative of order . Moreover, we obtain the necessary and sufficient conditions on data in order to have a unique solution by using recent results obtained for the fractional diffusion equation exploiting the properties of the Wright and Mainardi functions, given in: 1) Roscani-Santillan Marcus, Fract. Calc. Appl. Anal., 16 (2013), 802 - 815;2) Roscani-Tarzia, Adv. Math. Sci. Appl., 24 (2014), 237 - 249 and 3) Voller, Int. J. Heat Mass Transfer, 74 (2014), 269 - 277. This work generalizes the method developed for the determination of unknown thermal coefficients for the classical Lamé-Clapeyron-Stefan problem given in Tarzia, Adv. Appl. Math., 3 (1982), 74 - 82, which is recovered by taking the limit when the order .