Well-posedness and asymptotic estimate for a diffusion equation with time-fractional derivative

Zhiyuan Li; Xinchi Huang; Masahiro Yamamoto

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arXiv · 2108.11307

Well-posedness and asymptotic estimate for a diffusion equation with time-fractional derivative

Zhiyuan Li·Xinchi Huang·Masahiro Yamamoto

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Abstract

In this paper, we study the asymptotic estimate of solution for a mixed-order time-fractional diffusion equation in a bounded domain subject to the homogeneous Dirichlet boundary condition. Firstly, the unique existence and regularity estimates of solution to the initial-boundary value problem are considered. Then combined with some important properties, including a maximum principle for a time-fractional ordinary equation and a coercivity inequality for fractional derivatives, the energy method shows that the decay in time of the solution is dominated by the term $t^{-\alpha}$ as $t\to\infty$.

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Zhiyuan Li, Xinchi Huang, Masahiro Yamamoto. 2021-08-25. Well-posedness and asymptotic estimate for a diffusion equation with time-fractional derivative. https://arxiv.org/abs/2108.11307

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