arXiv subjects

Marlène Frigon

Publications and source records attributed to Marlène Frigon.

2 recordsLinked to original sources

arXiv2025

Stieltjes differential systems with non monotonic derivators

In this work we study Stieltjes differential systems of which the derivators are allowed to change sign. This leads to the definition of the notion of \emph{function of controlled variation}, a characterization of precompact sets of $g$-continuous functions, and an explicit expression of $g$-exponential maps. Finally, we prove a Peano-type existence result and apply it to a model of fluid stratification on buoyant miscible jets and plumes.

math.CA↗

arXiv2024

Prolongation of solutions and Lyapunov stability for Stieltjes dynamical systems

In this article, we introduce Lyapunov-type results to investigate the stability of the trivial solution of a Stieltjes dynamical system. We utilize prolongation results to establish the global existence of the maximal solution. Using Lyapunov's second method, we establish results of (uniform) stability and (uniform) asymptotic stability by employing a Lyapunov function. Additionally, we present examples and real-life applications to study asymptotic stability of equilibria in two population dynamics models.

math.CA↗