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arXiv · 2609.18814

Inverse problems for the diffusion equation with one time observation

Michel Cristofol·Alexandre Kawano
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Abstract

We examine the inverse problem of recovering the potential term of an n-dimensional heat equation from a single time solution profile. We show that it is possible to uniquely determine this potential term via a stability inequality using solution measurements taken at a fixed time, assuming the potential is known within an arbitrary subdomain. The approach is based on the Carleman estimate. Additionally, we discuss the optimality of this type of observation.

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Michel Cristofol, Alexandre Kawano. 2026-09-16. Inverse problems for the diffusion equation with one time observation. https://arxiv.org/abs/2609.18814

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