English

Magnetostatic levitation and two related linear PDEs in unbounded domains

Analysis of PDEs 2023-07-25 v3

Abstract

We consider a problem occurring in a magnetostatic levitation. The problem leads to a linear PDE in a strip. In engineering literature a particular solution is obtained. Such a solution enables one to compute lift and drag forces of the levitating object. It is in agreement with the experiment. We show that such a solution is unique in a class of bounded regular functions. Moreover, as a byproduct, we obtain nonstandard uniqueness results in two linear PDEs in unbounded domains. One of them is an Eigenvalue problem for the Laplacian in the strip in the nonstandard class of functions.

Keywords

Cite

@article{arxiv.2202.01570,
  title  = {Magnetostatic levitation and two related linear PDEs in unbounded domains},
  author = {Bartosz Bieganowski and Tomasz Cieślak and Jakub Siemianowski},
  journal= {arXiv preprint arXiv:2202.01570},
  year   = {2023}
}