RT Journal Article
T1 Mathematical analysis of a levitation model
A1 Muñoz Sola, Rafael
K1 Levitation model
K1 Transient eddy current problem
K1 Degenerate parabolic problem
K1 Axisymmetric geometry
K1 Moving domain
AB The aim of this paper is to study a model of electromagnetic levitation for a metallic rigid body. The model is constituted by the transient linear model of eddy currents under the hypothesis of axisymmetry, written in terms of a magnetic potential vector, coupled with an ODE which governs the vertical motion of the body. The electromagnetic model is a parabolic-elliptic PDE which parabolicity region is the position occupied by the body, which changes with time. Besides, Lorentz force appears in the RHS of the ODE. Thus, the model exhibits a coupling of geometrical nature. We establish the existence and uniqueness of solution of the coupled problem and we study its maximally defined solution. In particular, we prove that a blow-up of the velocity of the body cannot happen. Our techniques involve: a reformulation of the coupled problem as a causal differential equation, an adaptation of the theory about this kind of equations and a result of locally Lipschitz dependence of the magnetic potential vector with respect to the velocity of the body.
PB Elsevier
SN 1468-1218
YR 2025
FD 2025-12-23
LK https://hdl.handle.net/10347/46379
UL https://hdl.handle.net/10347/46379
LA eng
NO Muñoz-Sola, R. (2026). Mathematical analysis of a levitation model. Nonlinear Analysis: Real World Applications. https://doi.org/10.1016/j.nonrwa.2025.104573
DS Minerva
RD 24 abr 2026