An inverse problem for distributed order time-fractional diffusion equations
An inverse problem for distributed order time-fractional diffusion equations
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发表时间：
2017-07
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通讯作者：
Zhi-yuan Li;Kenichi Fujishiro;Gongsheng Li
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作者：
Zhi-yuan Li;Kenichi Fujishiro;Gongsheng Li
本文讨论了具有非齐次Dirichlet(Nuemann)边界条件的分布阶时间分数阶扩散方程。首先利用特征函数展开的方法证明了分布阶时间分数阶扩散方程初边值问题弱解的适定性，从而保证了弱解具有经典导数。其次，我们给出了在Laplace变换下频域解的一个Harnack型不等式，由此我们进一步证明了由点观测确定分布阶时间导数中的权函数反问题的唯一性结果。
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.