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arXiv · 2311.03540

Determination of source terms and coefficients dependent on $n-1$ spatial variable of parabolic and Schr\"odinger equations

Oleg Imanuvilov·Masahiro Yamamoto
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Abstract

We establish the uniqueness in the determination of a source term or a coefficient of the zeroth order term of a second-order parabolic equation. Moreover we consider the determination of a potential of the Schr\"odinger equation. For a parabolic equation, an unknown source term and coefficient depend on the time and $n-1$ spatial variables. For the Schr\"odinger equation, we assume that a potential depends on $n-1$ spatial variables. The data are taken on a part of the boundary satisfying some geometric condition.

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Oleg Imanuvilov, Masahiro Yamamoto. 2023-11-06. Determination of source terms and coefficients dependent on $n-1$ spatial variable of parabolic and Schr\"odinger equations. https://arxiv.org/abs/2311.03540

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