Long-time asymptotic of the Lifshitz-Slyozov equation with nucleation

Juan Calvo (1) , Erwan Hingant (2) , Romain Yvinec (3, 4)

1 UGR - Universidad de Granada = University of Granada
2 LAMFA - Laboratoire Amiénois de Mathématique Fondamentale et Appliquée - UMR CNRS 7352
3 MUSCA - Dynamiques de populations multi-échelles pour des systèmes physiologiques
4 PRC - Physiologie de la reproduction et des comportements [Nouzilly]

We consider the Lifshitz-Slyozov model with inflow boundary conditions of nucleation type. We show that for a collection of representative rate functions the size distributions approach degenerate states concentrated at zero size for sufficiently large times. The proof relies on monotonicity properties of some quantities associated to an entropy functional. Moreover, we give numerical evidence on the fact that the convergence rate to the goal state is algebraic in time. Besides their mathematical interest, these results can be relevant for the interpretation of experimental data.

Mots clés: nonlocal transport; Lifshitz-Slyozov equation; Entropy functional; Nucleation theory; Long-time behavior

Domaines: Equations aux dérivées partielles [math.AP]

Juan Calvo, Erwan Hingant, Romain Yvinec. Long-time asymptotic of the Lifshitz-Slyozov equation with nucleation. Kinetic and Related Models , In press, ⟨10.3934/krm.2023041⟩. ⟨hal-04098262v2⟩