DOI: 10.1515/jiip-2026-0032 ISSN: 0928-0219

Determination of source terms and coefficients dependent on n - 1 spatial variables of parabolic and Schrödinger 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 Schrödinger equation. For a parabolic equation, an unknown source term and an unknown coefficient depend on the time and

n - 1 n-1
spatial variables. For the Schrödinger equation, we assume that a potential depends on
n - 1 n-1
spatial variables. The data are taken on a part of the boundary satisfying some geometric condition.

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