Strong maximum principle for fractional diffusion equations and an application to an inverse source problem
Strong maximum principle for fractional diffusion equations and an application to an inverse source problem
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DOI：
10.1515/fca-2016-0048
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发表时间：
2015-07
影响因子：
3
通讯作者：
Yikan Liu;W. Rundell;Masahiro Yamamoto
中科院分区：
文献类型：
--
作者：
Yikan Liu;W. Rundell;Masahiro Yamamoto
摘要强极大值原理是抛物型方程的一个显著性质，分数阶扩散方程有望部分继承这一性质。基于相应的弱最大值原理，本文建立了含Caputo导数的时间分数阶扩散方程的一个强最大值原理，它比抛物型方程的强最大值原理稍弱.作为一个直接的应用，我们给出了一个相关的反源问题的非齐次项的时间分量的确定的唯一性结果。
Abstract The strong maximum principle is a remarkable property of parabolic equations, which is expected to be partly inherited by fractional diffusion equations. Based on the corresponding weak maximum principle, in this paper we establish a strong maximum principle for time-fractional diffusion equations with Caputo derivatives, which is slightly weaker than that for the parabolic case. As a direct application, we give a uniqueness result for a related inverse source problem on the determination of the temporal component of the inhomogeneous term.