15 citations · 38 across the 10 of their papers we have counts for
6 papers · 1 filter
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…
Analysis of a one dimensional energy dissipating free boundary model with nonlinear boundary conditions. Existence of weak solutions
Benoît Merlet, Juliette Venel, Antoine Zurek
This work is part of a general study on the long-term safety of the geological repository of nuclear wastes. A diffusion equation with a moving free boundary in one dimension is in…
Mathematical analysis of a thermodynamically consistent reduced model for iron corrosion
Clément Cancès, Claire Chainais-Hillairet, Benoît Merlet +2
We are interested in a reduced model for corrosion of iron, in which ferric cations and electrons evolve in a fixed oxide layer subject to a self-consistent electrostatic potential…
Sweeping process by prox-regular sets in Riemannian Hilbert manifolds
Frédéric Bernicot, Juliette Venel
In this paper, we deal with sweeping processes on (possibly infinite-dimensional) Riemannian Hilbert manifolds. We extend the useful notions (proximal normal cone, prox-regularity)…
Existence of solutions for second-order differential inclusions involving proximal normal cones
Frederic Bernicot, Juliette Venel
In this work, we prove global existence of solutions for second order differential problems in a general framework. More precisely, we consider second order differential inclusions…
Stochastic perturbation of sweeping process and a convergence result for an associated numerical scheme
Frederic Bernicot, Juliette Venel
Here we present well-posedness results for first order stochastic differential inclusions, more precisely for sweeping process with a stochastic perturbation. These results are pro…