Determination of source terms and coefficients dependent on $n-1$ spatial variable of parabolic and Schr\"odinger equations
Analysis of PDEs
2023-11-08 v1
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 spatial variables. For the Schr\"odinger equation, we assume that a potential depends on spatial variables. The data are taken on a part of the boundary satisfying some geometric condition.
Keywords
Cite
@article{arxiv.2311.03540,
title = {Determination of source terms and coefficients dependent on $n-1$ spatial variable of parabolic and Schr\"odinger equations},
author = {Oleg Imanuvilov and Masahiro Yamamoto},
journal= {arXiv preprint arXiv:2311.03540},
year = {2023}
}