An inverse problem for a fractional diffusion equation with fractional power type nonlinearities

Li Li

doi:10.3934/ipi.2021064

Article Contents

2022, Volume 16, Issue 3: 613-624. Doi: 10.3934/ipi.2021064

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An inverse problem for a fractional diffusion equation with fractional power type nonlinearities

Li Li^,

Institute for Pure and Applied Mathematics, University of California, Los Angeles, CA 90095, USA

^*Corresponding author: Li Li
^*Corresponding author: Li Li

Received: April 2021

Revised: August 2021

Early access: October 2021

Published: June 2022

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Abstract

We study the well-posedness of a semi-linear fractional diffusion equation and formulate an associated inverse problem. We determine fractional power type nonlinearities from the exterior partial measurements of the Dirichlet-to-Neumann map. Our arguments are based on a first order linearization as well as the parabolic Runge approximation property.

Keywords:

Inverse problem,
nonlinear fractional parabolic operator,
Runge approximation property.

Mathematics Subject Classification: Primary: 35R11, 35R30.

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