Regular solutions to the coagulation equations with singular kernels | Zendy

Camejo Carlos Cueto | Zendy; Gröpler Robin | Zendy; Warnecke Gerald | Zendy

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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.

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