English

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 n1n-1 spatial variables. For the Schr\"odinger equation, we assume that a potential depends on n1n-1 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}
}