Studies on an inverse source problem for a space-time fractional diffusion equation by constructing a strong maximum principle
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.
Cite
@article{arxiv.1606.01378,
title = {Studies on an inverse source problem for a space-time fractional diffusion equation by constructing a strong maximum principle},
author = {Junxiong Jia and Jigen Peng and Jiaqing Yang},
journal= {arXiv preprint arXiv:1606.01378},
year = {2016}
}
Comments
30 pages. arXiv admin note: text overlap with arXiv:1009.4852 by other authors