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arXiv · 2202.01570

Magnetostatic levitation and two related linear PDEs in unbounded domains

Bartosz Bieganowski·Tomasz Cieślak·Jakub Siemianowski
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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.

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Bartosz Bieganowski, Tomasz Cieślak, Jakub Siemianowski. 2022-02-03. Magnetostatic levitation and two related linear PDEs in unbounded domains. https://arxiv.org/abs/2202.01570

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