Weak solutions to the continuous coagulation equation with multiple fragmentation

Ankik Kumar Giri; Philippe Laurençot; Gerald Warnecke

doi:10.1016/j.na.2011.10.021

Weak solutions to the continuous coagulation equation with multiple fragmentation

Nonlinear Anal Theory Methods Appl. 2012 Mar;75(4):2199-2208. doi: 10.1016/j.na.2011.10.021.

Authors

Ankik Kumar Giri¹, Philippe Laurençot, Gerald Warnecke

Affiliation

¹ Institute for Applied Mathematics, Montan University Leoben, Franz Josef Straße 18, A-8700 Leoben, Austria.

Abstract

The existence of weak solutions to the continuous coagulation equation with multiple fragmentation is shown for a class of unbounded coagulation and fragmentation kernels, the fragmentation kernel having possibly a singularity at the origin. This result extends previous ones where either boundedness of the coagulation kernel or no singularity at the origin for the fragmentation kernel was assumed.