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math.AP2026

Discrete adjoint gradient computation for multiclass traffic flow models on road networks

Paola Goatin, Axel Klar, Carmen Mezquita-Nieto

This paper applies a discrete adjoint gradient computation method for a multi-class traffic flow model on road networks. Vehicle classes are characterized by their specific velocit…

math.AP2025

Structured Continuity Equations in Fibred Wasserstein Spaces

Benoît Bonnet-Weill, Nastassia Pouradier Duteil

In this article, we develop a comprehensive ODE-theory for structured continuity equations in fibred probability spaces, which represent a class of heterogeneous PDEs arising as th…

math.AP2025

Two-way Coupling of Fluid--Structure Interaction for Elastic Magneto-Swimmers:A Finite Element ALE Approach

Christophe Prud'Homme, Vincent Chabannes, Laëtitia Giraldi +2

Artificial micro-swimmers actuated by external magnetic fields hold significant promise for targeted biomedical applications, including drug delivery and micro-robot-assisted thera…

math.AP2025

Analysis of linear Boussinesq-type models coupled with static interfaces

José Galaz, Maria Kazolea, Antoine Rousseau

We derive a new approach to analyze the coupling of linear Boussinesq and Saint-Venant shallow water wave equations in the case where the interface remains at a constant position i…

math.AP2024★ 2 cited

Well-posedness and regularity of solutions to neural field problems with dendritic processing

Daniele Avitabile, Nikolai V. Chemetov, Pedro M. Lima

We study solutions to a recently proposed neural field model in which dendrites are modelled as a continuum of vertical fibres stemming from a somatic layer. Since voltage propagat…

math.AP2024★ 1 cited

On the blow-up scenario for some modified Serre-Green-Naghdi equations

Billel Guelmame

The present paper deals with a modified Serre-Green-Naghdi (mSGN) system that has been introduced by Clamond et al. to improve the dispersion relation. We present a precise blow-up…