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Summary: Local and Global Strong Solutions to
Continuous Coagulation-Fragmentation
Equations with Diffusion
Herbert Amann
Universit¨at Z¨urich, Institut f¨ur Mathematik, Winterthurerstr. 190, CH-8057
Z¨urich, Switzerland
Christoph Walker
Vanderbilt University, Department of Mathematics, 1326 Stevenson Center,
Nashville, TN 37240, USA
Abstract
We consider the diffusive continuous coagulation-fragmentation equations with and
without scattering and show that they admit unique strong solutions for a large
class of initial values. If the latter values are small with respect to a suitable norm,
we provide sufficient conditions for global-in-time existence in the absence of frag-
mentation.
Key words: coagulation, fragmentation, volume scattering, diffusion, semigroup
theory
1 Introduction
The present paper contributes to the mathematical investigation of coagula-
tion and fragmentation processes. Describing the mechanisms by which par-
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