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.
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Liu, Y., Rundell, W. & Yamamoto, M. Strong maximum principle for fractional diffusion equations and an application to an inverse source problem. FCAA 19, 888–906 (2016). https://doi.org/10.1515/fca-2016-0048
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DOI: https://doi.org/10.1515/fca-2016-0048