Studies on an inverse source problem for a space-time fractional diffusion equation by constructing a strong maximum principle

Junxiong Jia; Jigen Peng; Jiaqing Yang

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arXiv · 1606.01378

Studies on an inverse source problem for a space-time fractional diffusion equation by constructing a strong maximum principle

Junxiong Jia·Jigen Peng·Jiaqing Yang

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Abstract

In this paper, we focus on a space-time fractional diffusion equation with the generalized Caputo's fractional derivative operator and a general space nonlocal operator (with the fractional Laplace operator as a special case). A weak Harnack's inequality has been established by using a special test function and some properties of the space nonlocal operator. Based on the weak Harnack's inequality, a strong maximum principle has been obtained which is an important characterization of fractional parabolic equations. With these tools, we establish a uniqueness result for an inverse source problem on the determination of the temporal component of the inhomogeneous term.

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Junxiong Jia, Jigen Peng, Jiaqing Yang. 2016-06-04. Studies on an inverse source problem for a space-time fractional diffusion equation by constructing a strong maximum principle. https://arxiv.org/abs/1606.01378

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