Linearized uniqueness of space dependent coefficients in a non-autonomous evolution equation from non-local observations

Barbara Kaltenbacher

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arXiv · 2608.07177

Linearized uniqueness of space dependent coefficients in a non-autonomous evolution equation from non-local observations

Barbara Kaltenbacher

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Abstract

In this paper, we consider identification of space dependent coefficients in a time dependent PDE, which is non-autonomous, due to a bilinear control term. We prove linearized uniqueness from time trace observations, in particular also considering non-local observations in the form of weighted integrals of the state over he spatial domain. The result is obtained in an abstract setting and applied, first of all to the identification of a potential in a diffusion equation for illustration purposes, second to the reconstruction of equilibrium magnetization, relaxation rates and field inhomogeneity as space dependent quantities in model based qunatitative magnetic resonance imaging with the Bloch-Torrey equation, which constitutes the real world application motivating this study.

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Barbara Kaltenbacher. 2026-08-07. Linearized uniqueness of space dependent coefficients in a non-autonomous evolution equation from non-local observations. https://arxiv.org/abs/2608.07177

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