Year: 2026
Type: preprint
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 $C^{1,α}$-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 $n\ge2$ 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.
Source: arXiv (Cornell University)
Authors: Lin, Ching-Lung, Lin, Yi-Hsuan
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223667000