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PreprintCC BY 4.0Nonlinear Analysis: Theory, Methods and Applications

Inverse problems for the diffusion equation with one time observation

  • Michel Cristofol
  • Alexandre Kawano
Open at sourcePDFDOICite

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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Cite

BibTeXRIS
BibTeX
@misc{cristofol2026inverse,
  title = {{Inverse problems for the diffusion equation with one time observation}},
  author = {Michel Cristofol and Alexandre Kawano},
  howpublished = {Nonlinear Analysis: Theory, Methods and Applications},
  year = {2026},
  month = jul,
  doi = {10.48550/arxiv.2609.18814},
  eprint = {2609.18814},
  archivePrefix = {arXiv},
  url = {https://hal.science/hal-05743036v1},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Inverse problems for the diffusion equation with one time observation
AU  - Michel Cristofol
AU  - Alexandre Kawano
PY  - 2026
DA  - 2026/07/15
PB  - Nonlinear Analysis: Theory, Methods and Applications
DO  - 10.48550/arxiv.2609.18814
UR  - https://hal.science/hal-05743036v1
AB  - 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.
SN  - 0362-546X
SN  - 1873-5215
ER  -