Initial-boundary value problems for multi-term time-fractional diffusion equations with positive constant coefficients
Initial-boundary value problems for multi-term time-fractional diffusion equations with positive constant coefficients
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DOI：
10.1016/j.amc.2014.11.073
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发表时间：
2015-04-15
影响因子：
4
通讯作者：
Yamamoto, Masahiro
中科院分区：
文献类型：
--
作者：
Li, Zhiyuan;Liu, Yikan;Yamamoto, Masahiro
本文研究了多项时间分数阶扩散方程初边值问题的适定性和长时间渐近性态。所考虑的控制方程包括Caputo导数在时间上的线性组合，在（0，1）和正常系数中具有递减的阶数。利用多项Mittag-Leffler函数的几个重要性质，从这些特殊函数的显式解中得出各种估计。然后证明了解的唯一性和对初值和源项的连续依赖性，并由此进一步证明了解对分数阶导数的系数和阶数的Lipschitz连续依赖性.最后，通过拉普拉斯变换证明了当t ->无穷远时解的衰减率由时间分数阶导数的最小阶数给出. (C)2014爱思唯尔公司All rights reserved.
In this paper, we investigate the well-posedness and the long-time asymptotic behavior for initial-boundary value problems for multi-term time-fractional diffusion equations. The governing equation under consideration includes a linear combination of Caputo derivatives in time with decreasing orders in (0,1) and positive constant coefficients. By exploiting several important properties of multinomial Mittag-Leffler functions, various estimates follow from the explicit solutions in form of these special functions. Then we prove the uniqueness and continuous dependency on initial values and source terms, from which we further verify the Lipschitz continuous dependency of solutions with respect to coefficients and orders of fractional derivatives. Finally, by a Laplace transform argument, it turns out that the decay rate of the solution as t -> infinity is given by the minimum order of the time-fractional derivatives. (C) 2014 Elsevier Inc. All rights reserved.