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Regular solutions to the coagulation equations with singular kernels
Author(s) -
Camejo Carlos Cueto,
Gröpler Robin,
Warnecke Gerald
Publication year - 2014
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3211
Subject(s) - mathematics , uniqueness , gravitational singularity , kernel (algebra) , compact space , mathematical analysis , base (topology) , order (exchange) , pure mathematics , finance , economics
In this article, we prove the existence of solutions to the coagulation equation with singular kernels. We use weighted L 1 ‐spaces to deal with the singularities in order to obtain regular solutions. The Smoluchowski kernel is covered by our proof. The weak L 1 compactness methods are applied to suitably chosen approximating equations as a base of our proof. A more restrictive uniqueness result is also mentioned. Copyright © 2014 John Wiley & Sons, Ltd.