Uniqueness and reconstruction of an unknown semilinear term in a time-fractional reaction–diffusion equation
Uniqueness and reconstruction of an unknown semilinear term in a time-fractional reaction–diffusion equation
复制标题
DOI：
10.1088/0266-5611/29/6/065019
复制
发表时间：
2013-06
期刊：
影响因子：
2.1
通讯作者：
Yuri Luchko;W. Rundell;Masahiro Yamamoto;L. Zuo
中科院分区：
文献类型：
--
作者：
Yuri Luchko;W. Rundell;Masahiro Yamamoto;L. Zuo
在本文中，我们考虑了一个反应扩散问题与未知的非线性源函数，必须确定从重叠的数据。底层模型是时间分数阶反应扩散方程的形式，工作推广了抛物型偏微分方程反问题的一些已知结果。对于所考虑的反问题，证明了一个唯一性结果，并在一维情况下给出了一个具有一定理论条件的数值算法。唯一性结果和数值算法的关键都依赖于最近被证明对分数阶扩散方程成立的最大值原理。为了证明所提出的方法的有效性，数值模拟的结果。
In this paper, we consider a reaction–diffusion problem with an unknown nonlinear source function that has to be determined from overposed data. The underlying model is in the form of a time-fractional reaction–diffusion equation and the work generalizes some known results for the inverse problems posed for PDEs of parabolic type. For the inverse problem under consideration, a uniqueness result is proved and a numerical algorithm with some theoretical qualification is presented in the one-dimensional case. The key both to the uniqueness result and to the numerical algorithm relies on the maximum principle which has recently been shown to hold for the fractional diffusion equation. In order to show the effectiveness of the proposed method, results of numerical simulations are presented.