Asymptotic estimates of solutions to initial-boundary-value problems for distributed order time-fractional diffusion equations

By Zhi-yuan Li, Yuri Luchko, Masahiro Yamamoto. 2014

93 citations recorded by the source corpus.

This article deals with investigation of some important properties of solutions to initial-boundary-value problems for distributed order time-fractional diffusion equations in bounded multi-dimensional domains. In particular, we investigate the asymptotic behavior of the solutions as the time variable t → 0 and t → +∞. By the Laplace transform method, we show that the solutions decay logarithmically as t → +∞. As t → 0, the decay rate of the solutions is dominated by the term (t log(1/t))−1. Thus the asymptotic behavior of solutions to the initial-boundary-value problem for the distributed order time-fractional diffusion equations is shown to be different compared to the case of the multi-term fractional diffusion equations.

Subfields: Applied Mathematics, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/ebe383b0ea034a9014fa4194ae24d01eaab2efce

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In Applied Mathematics

1. Shengda Zeng
2. Yunru Bai
3. Zhenhai Liu
4. Patrick Winkert
5. Csaba Farkas

In Modeling and Simulation

1. Yunru Bai
2. Shengda Zeng
3. Zhenhai Liu

In Numerical Analysis

1. Shengda Zeng
2. Yunru Bai
3. Zhenhai Liu

Citations in the corpus

• Maximum Principles for Multi-Term Space-Time Variable-Order Fractional Diffusion Equations and their Applications (2016, background): “For more details on this topics the reader is welcome to consult [6, 13, 14, 15, 16, 17, 18] and the references therein.”