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Inverse problems for the heat equation with memory

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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  • 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.

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


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