An inverse problem and a time-like Carleman estimate for parabolic integro-differential equations

Atsushi Kawamoto

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arXiv · 1710.03674

An inverse problem and a time-like Carleman estimate for parabolic integro-differential equations

Atsushi Kawamoto

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Abstract

In this article, We investigate an inverse problem of determining the time-dependent source factor in parabolic integro-differential equations from boundary data. We establish the uniqueness and the conditional stability estimate of H\"older type for the inverse source problem in a cylindrical shaped domain. Our methodology is based on the Bukhgeim-Klibanov method by means of the Carleman estimate. Here we also derive the "time-like" Carleman estimate for parabolic integro-differential equations.

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Atsushi Kawamoto. 2017-10-10. An inverse problem and a time-like Carleman estimate for parabolic integro-differential equations. https://arxiv.org/abs/1710.03674

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