Large time behavior and Lyapunov functionals for a nonlocal differential equation

Danielle Hilhorst (1) , Philippe Laurençot (2) , Thanh-Nam Nguyen (3)

1 LM-Orsay - Laboratoire de Mathématiques d'Orsay
2 IMT - Institut de Mathématiques de Toulouse UMR5219
3 National Institute for Mathematical Sciences, Daejeon

A new approach is used to describe the large time behavior of the non-local differential equation initially studied in [3]. Our approach is based upon the existence of infinitely many Lyapunov functionals and allows us to extend the analysis performed in [3].

Mots clés: Nonlocal differential equation; ω-limit set; large time behavior; convergence to steady states

Domaines: Equations aux dérivées partielles [math.AP]

Danielle Hilhorst, Philippe Laurençot, Thanh-Nam Nguyen. Large time behavior and Lyapunov functionals for a nonlocal differential equation. Nonlinear Differential Equations and Applications, 2016, 23, pp.30. ⟨hal-01224734⟩