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arXiv · 2411.02901

Two parabolic inverse problems for an equation with unbounded zero-order coefficient

Mourad Choulli
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Abstract

This work is composed of two parts. We prove in the first part the uniqueness of the determination of the unbounded zero-order coefficient in a parabolic equation from boundary measurements. The novelty of our result is that it covers the largest class of unbounded zero-order coefficients. We establish in the second part a logarithmic stability inequality for the problem of determining the initial condition from a single interior measurement. As by-product, we obtain an observability inequality for a parabolic equation with unbounded zero-order coefficient. The proof of this observability inequality is based on a new global quantitative unique continuation for the Schr\"odinger equation with unbounded potential. For the sake of completeness, we provide in Appendix A a full proof of this result.

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Mourad Choulli. 2024-11-05. Two parabolic inverse problems for an equation with unbounded zero-order coefficient. https://arxiv.org/abs/2411.02901

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