Viscous scalar conservation law with stochastic forcing: strong solution and invariant measure

Autor: Julien Reygner, Sofiane Martel

Publikováno v: Nonlinear Differential Equations and Applications
Nonlinear Differential Equations and Applications, Springer Verlag, 2020, 27, pp.34. ⟨10.1007/s00030-020-00637-9⟩
Nonlinear Differential Equations and Applications, 2020, 27, pp.34. ⟨10.1007/s00030-020-00637-9⟩

We are interested in viscous scalar conservation laws with a white-in-time but spatially correlated stochastic forcing. The equation is assumed to be one-dimensional and periodic in the space variable, and its flux function to be locally Lipschitz co

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::122ef4df2bf08315e3faa317606bdae2
https://hal.archives-ouvertes.fr/hal-02133338

Numerical schemes for the aggregation equation with pointy potentials

Autor: François Delarue, Sofiane Martel, Frédéric Lagoutière, Kévin Le Balc'h, Hélène Hivert, Nicolas Vauchelet, Benoît Fabrèges

Publikováno v: ESAIM: Proceedings and Surveys
ESAIM: Proceedings and Surveys, EDP Sciences, 2019, ⟨10.1051/proc/201965384⟩
ESAIM: Proceedings and Surveys, Vol 65, Pp 384-400 (2019)
ESAIM: Proceedings and Surveys, 2019, ⟨10.1051/proc/201965384⟩

International audience; The aggregation equation is a nonlocal and nonlinear conservation law commonly used to describe the collective motion of individuals interacting together. When interacting potentials are pointy, it is now well established that

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f50bf2778b0721635901bd4605dc739a
https://hal.archives-ouvertes.fr/hal-01788050