Uniqueness for an inverse problem for a semilinear time-fractional diffusion equation

Jaan Janno; Kairi Kasemets

doi:10.3934/ipi.2017007

Article Contents

2017, Volume 11, Issue 1: 125-149. Doi: 10.3934/ipi.2017007

This issue Previous Article On finding an obstacle with the Leontovich boundary condition via the time domain enclosure method Next Article Non-linear Tikhonov regularization in Banach spaces for inverse scattering from anisotropic penetrable media

Uniqueness for an inverse problem for a semilinear time-fractional diffusion equation

Jaan Janno and
Kairi Kasemets

Tallinn University of Technology, Ehitajate tee 5, Tallinn 19086, Estonia

Received: October 31, 2015

Revised: May 31, 2016

Published: March 2018

The research is supported by the Estonian Research Council grant PUT568 and institutional research funding IUT33-24 of the Estonian Ministry of Education and Research

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Abstract

An inverse problem to determine a space-dependent factor in a semilinear time-fractional diffusion equation is considered. Additional data are given in the form of an integral with the Borel measure over the time. Uniqueness of the solution of the inverse problem is studied. The method uses a positivity principle of the corresponding differential equation that is also proved in the paper.

Keywords:

Inverse problem,
fractional diffusion,
semilinear fractional parabolic equation,
uniqueness,
positivity principle.

Mathematics Subject Classification: Primary: 35R30; Secondary: 80A23.

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References

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