Inverse problems for the heat equation with memory

Sergei A. Avdonin; Sergei A. Ivanov; Jun-Min Wang

doi:10.3934/ipi.2019002

Article Contents

2019, Volume 13, Issue 1: 31-38. Doi: 10.3934/ipi.2019002

This issue Previous Article Hyperpriors for Matérn fields with applications in Bayesian inversion Next Article Magnetic moment estimation and bounded extremal problems

Inverse problems for the heat equation with memory

1.
University of Alaska, Fairbanks, AK 99775-6660, USA
2.
Russian Academy of Sciences, St. Petersburg, Mendeleev line 1, Russia
3.
Beijing Institute of Technology, Beijing 100081, China

Received: August 2017

Revised: October 2018

Published: December 2018

The first author is supported by the NSF, grant DMS 1411564, and by the Ministry of Education and Science of Republic of Kazakhstan under the grant no. AP05136197.

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Abstract

We study inverse boundary problems for one dimensional linear integro-differential equation of the Gurtin-Pipkin type with the Dirichlet-to-Neumann map as the inverse data. Under natural conditions on the kernel of the integral operator, we give the explicit formula for the solution of the problem with the observation on the semiaxis t>0. For the observation on finite time interval, we prove the uniqueness result, which is similar to the local Borg-Marchenko theorem for the Schrödinger equation.

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Mathematics Subject Classification: Primary: 45K05; Secondary: 35P20.

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References

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