CONVERGENCE OF A LINEARLY TRANSFORMED PARTICLE METHOD FOR AGGREGATION EQUATIONS

Martin Campos Pinto (1) , José Antonio Carrillo de La Plata (2) , Frédérique Charles (1, 3) , Young-Pil Choi (2)

1 LJLL - Laboratoire Jacques-Louis Lions
2 Department of Mathematics [Imperial College London]
3 SU - Sorbonne Université

We study a linearly transformed particle method for the aggre-gation equation with smooth or singular interaction forces. For the smooth interaction forces, we provide convergence estimates in L 1 and L ∞ norms depending on the regularity of the initial data. Moreover, we give convergence estimates in bounded Lipschitz distance for measure valued solutions. For singular interaction forces, we establish the convergence of the error between the approximated and exact flows up to the existence time of the solutions in L 1 ∩ L p norm.

Mots clés: Aggregation equation; linearly transformed particle method; smooth and singular interaction potentials

Domaines: Equations aux dérivées partielles [math.AP]

Martin Campos Pinto, José Antonio Carrillo de La Plata, Frédérique Charles, Young-Pil Choi. CONVERGENCE OF A LINEARLY TRANSFORMED PARTICLE METHOD FOR AGGREGATION EQUATIONS. Numerische Mathematik, 2018, 139, pp.743-793. ⟨hal-01180687⟩