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Applicable Analysis
An International Journal
Volume 99, 2020 - Issue 15
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Articles

Well-posedness for a nonlocal nonlinear diffusion equation and applications to inverse problems

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Pages 2609-2623 | Received 15 Jul 2018, Accepted 22 Jan 2019, Published online: 11 Feb 2019
 

ABSTRACT

This article investigates a space–time fractional diffusion equation with a nonlinear source and a space nonlocal operator. The well-posedness is demonstrated from using contraction mapping theorem and generalized Gronwall's inequality firstly. Based on the forward problem, we prove that a nonlinear source term and a fractional order of time derivative are uniquely determined by data which can be observed at one fixed spatial point.

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2010 Mathematics Subject Classifications:

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported in part by the National Natural Science Foundation of China [Grants Nos 11871392, 11771347, 91730306, 41390454].

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