An inverse problem for distributed order time-fractional diffusion equations
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.
Cite
@article{arxiv.1707.02556,
title = {An inverse problem for distributed order time-fractional diffusion equations},
author = {Zhiyuan Li and Kenichi Fujishiro and Gongsheng Li},
journal= {arXiv preprint arXiv:1707.02556},
year = {2018}
}
Comments
In the previous version, our result was proved provide upon Dirichlet boundary condition. Now we generalized the result to the Nuemann case