A Carleman type estimate of variable order space-fractional diffusion equations and applications to some inverse problems

Junxiong Jia; Jigen Peng

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arXiv · 1610.06680

A Carleman type estimate of variable order space-fractional diffusion equations and applications to some inverse problems

Junxiong Jia·Jigen Peng

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Abstract

Variable order space-fractional diffusion equation derived as an important model to describe complex anomalous diffusion phenomenon. In this article, well-posedness theory has been constructed for equations with the "Dirichlet" or the "Neumann" type volume-constrained conditions by using the technique of the nonlocal vector calculus. Then some regularity properties have been obtained under the variable-order Sobolev space framework. By choosing a space-independent weight function and using the technique of the nonlocal vector calculus, a Carleman type estimate has been obtained. At last, the Carleman type estimate has been used both to a backward diffusion problem and an inverse source problem to obtain some uniqueness and stability results.

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Junxiong Jia, Jigen Peng. 2016-10-21. A Carleman type estimate of variable order space-fractional diffusion equations and applications to some inverse problems. https://arxiv.org/abs/1610.06680

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