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6 papers · 2 filters
Longtime and chaotic dynamics in microscopic systems with singular interactions
Alexis Béjar-López, Alain Blaustein, Pierre-Emmanuel Jabin +1
This paper investigates the long time dynamics of interacting particle systems subject to singular interactions. We consider a microscopic system of interacting point particles…
Continuum of coupled Wasserstein gradient flows
Clément Cancès, Daniel Matthes, Ismael Medina +1
We study a system of drift-diffusion PDEs for a potentially infinite number of incompressible phases, subject to a joint pointwise volume constraint. Our analysis is based on the i…
Discretizing the Fokker-Planck equation with second-order accuracy: a dissipation driven approach
Clément Cancès, Léonard Monsaingeon, Andrea Natale
We propose a fully discrete finite volume scheme for the standard Fokker-Planck equation. The space discretization relies on the well-known square-root approximation, which falls i…
Charge transport systems with Fermi-Dirac statistics for memristors
Maxime Herda, Ansgar Jüngel, Stefan Portisch
An instationary drift-diffusion system for the electron, hole, and oxygen vacancy densities, coupled to the Poisson equation for the electric potential, is analyzed in a bounded do…
Well-posedness and long-time behavior for self-consistent Vlasov-Fokker-Planck equations with general potentials
Pierre Gervais, Maxime Herda
We study the well-posedness, steady states and long time behavior of solutions to Vlasov-Fokker-Planck equation with external confinement potential and nonlinear self-consistent in…
Frequency-explicit stability estimates for time-harmonic elastodynamic problems in nearly incompressible materials
T. Chaumont-Frelet, S. Nicaise
We consider time-harmonic elastodynamic problems in heterogeneous media.cWe focus on scattering problems in the high-frequency regime and incnearly incompressible media, where the…