An inverse problem for distributed order time-fractional diffusion equations

Zhiyuan Li; Kenichi Fujishiro; Gongsheng Li

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arXiv · 1707.02556

An inverse problem for distributed order time-fractional diffusion equations

Zhiyuan Li·Kenichi Fujishiro·Gongsheng Li

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Abstract

This paper deals with the distributed order time-fractional diffusion equations with non-homogeneous Dirichlet (Nuemann) boundary condition. We first prove the wellposedness of the weak solution to the initial boundary value problem for the distributed order time-fractional diffusion equation by means of eigenfunction expansion, which ensure that the weak solution has the classical derivatives. We next give a Harnack type inequality of the solution in the frequency domain under the Laplace transform, from which we further show a uniqueness result for an inverse problem in determining the weight function in the distributed order time derivative from point observation.

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Zhiyuan Li, Kenichi Fujishiro, Gongsheng Li. 2017-07-09. An inverse problem for distributed order time-fractional diffusion equations. https://arxiv.org/abs/1707.02556

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