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math.AP2026
Multiple solutions and simulations for an Ion Flow Field problem applied to HVDC transmission lines
Madeline Chauvier, Serge Nicaise, Christophe Troestler +1
This paper initiates a mathematical investigation of a PDE model for the transport of high voltage direct current via overhead lines. We prove the existence of infinitely many solu…
math.AP2026
Blow-up analysis and a priori bounds for NLS equations on metric graphs
Pablo Carrillo, Colette De Coster, Damien Galant +2
We consider, on a connected metric graph , a family of nonlinear Schrödinger equations $$ -u'' + W_n(x) u + λ_n u = ρ_n(x)|u|^{p-2}u, \quad n \in \mathbb{N}. \qquad (*…