{"ID":22973661,"CreatedAt":"2026-09-17T02:46:45.862280177Z","UpdatedAt":"2026-09-17T02:46:45.862280177Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2609.18814","arxiv_id":"2609.18814","title":"Inverse problems for the diffusion equation with one time observation","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.","short_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 withi...","url_abs":"https://arxiv.org/abs/2609.18814","url_pdf":"https://arxiv.org/pdf/2609.18814v1","authors":"[\"Michel Cristofol\",\"Alexandre Kawano\"]","published":"2026-09-16T15:22:42Z","proceeding":"math.AP","tasks":"[\"math.AP\"]","methods":"[\"Diffusion Model\"]","has_code":false}