Hölder stability estimate in an inverse source problem for a first and half order time fractional diffusion equation

Atsushi Kawamoto

doi:10.3934/ipi.2018014

Article Contents

2018, Volume 12, Issue 2: 315-330. Doi: 10.3934/ipi.2018014

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Hölder stability estimate in an inverse source problem for a first and half order time fractional diffusion equation

Atsushi Kawamoto

Department of Mathematical Sciences, The University of Tokyo, Komaba Meguro Tokyo 153-8914, Japan

Received: October 31, 2016

Revised: October 31, 2017

Published: March 2018

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Abstract

We consider the first and half order time fractional equation with the zero initial condition. We investigate an inverse source problem of determining the time-independent source factor by the spatial data at an arbitrarily fixed time and we establish the conditional stability estimate of Hölder type in our inverse problem. Our method is based on the Bukhgeim-Klibanov method by means of the Carleman estimate. We also derive the Carleman estimate for the first and half order time fractional diffusion equation.

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Mathematics Subject Classification: Primary: 35R11, 35R30; Secondary: 35B35.

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