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PreprintarXiv licencearXiv

Global recovery of a scalar diffusivity from a single final state

  • Ching-Lung Lin
  • Yi-Hsuan Lin
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Abstract

We prove global uniqueness and Lipschitz stability for a scalar diffusivity in the heat equation from a single final state at any prescribed positive time. On each prescribed uniformly elliptic C1,α-bounded class with known coefficient boundary values, we choose a constant initial datum and a spatially constant exponential boundary input that work for the entire class. The result holds on smooth bounded connected domains in every dimension n≥2 and gives an affirmative answer to \cite[Problem~8.2]{Alessandrini} within these classes. The stability estimate controls the L2 diffusivity difference by the H2 final-state difference, and this data norm is optimal within the Sobolev scale for the chosen experiment.

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Cite

BibTeXRIS
BibTeX
@misc{lin2026global,
  title = {{Global recovery of a scalar diffusivity from a single final state}},
  author = {Ching-Lung Lin and Yi-Hsuan Lin},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.32063},
  eprint = {2610.32063},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.32063},
}
RIS
TY  - UNPB
TI  - Global recovery of a scalar diffusivity from a single final state
AU  - Ching-Lung Lin
AU  - Yi-Hsuan Lin
PY  - 2026
DA  - 2026/10/23
PB  - arXiv
DO  - 10.48550/arxiv.2610.32063
UR  - https://arxiv.org/abs/2610.32063
AB  - We prove global uniqueness and Lipschitz stability for a scalar diffusivity in the heat equation from a single final state at any prescribed positive time. On each prescribed uniformly elliptic C^1,α-bounded class with known coefficient boundary values, we choose a constant initial datum and a spatially constant exponential boundary input that work for the entire class. The result holds on smooth bounded connected domains in every dimension n≥2 and gives an affirmative answer to \cite[Problem~8.2]{Alessandrini} within these classes. The stability estimate controls the L^2 diffusivity difference by the H^2 final-state difference, and this data norm is optimal within the Sobolev scale for the chosen experiment.
ER  -