Determination of source terms and coefficients dependent on n-1 spatial variable of parabolic and Schrödinger equations

2023/11/06 by Imanuvilov, Oleg, Yamamoto, Masahiro
#35 #35R30 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2311.03540

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 coefficient depend on the time and n-1 spatial variables. For the Schrödinger 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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