# An Inverse Problem for the Porous Medium Equation with Partial Data and a Possibly Singular Absorption Term

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**Submitted**: 15 December 2021

**Accepted**: 6 September 2022

**Published online**: 28 January 2023

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**Funding:**The work of the first author was supported by the National Natural Science Foundation of China grants 11931011, 11971333. The work of the second author was supported by the Collaborative Research Center, membership 1283, Universitat Bielefeld. The work of the third author was partially supported by the National Science Foundation, a Walker Family Professorship at the University of Washington, a Si Yuan Professorship at IAS, HKUST, and a Simons Foundation Fellowship. Part of this work was done while the third author was visiting IPAM in Fall 2021.

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