Applications of improved duality lemmas to the discrete coagulation-fragmentation equations with diffusion

Maxime Breden

doi:10.3934/krm.2018014

Article Contents

2018, Volume 11, Issue 2: 279-301. Doi: 10.3934/krm.2018014

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Applications of improved duality lemmas to the discrete coagulation-fragmentation equations with diffusion

Maxime Breden^1,2,

1.
CMLA, ENS Cachan, CNRS, Université Paris-Saclay, 94235 Cachan, France
2.
Technical University of Munich, Faculty of Mathematics, Research Unit "Multiscale and Stochastic Dynamics", 85748 Garching b. München, Germany

Received: February 2017

Published: April 2018

The author was partially supported by french "ANR blanche" project Kibord: ANR-13-BS01-0004

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Abstract

In this paper, we investigate the use of so called "duality lemmas" to study the system of discrete coagulation-fragmentation equations with diffusion. When the fragmentation is strong enough with respect to the coagulation, we show that we have creation and propagation of superlinear moments. In particular this implies that strong enough fragmentation can prevent gelation even for superlinear coagulation, a statement which was only known up to now in the homogeneous setting. We also use this control of superlinear moments to extend a recent result from [3], about the regularity of the solutions in the pure coagulation case, to strong fragmentation models.

Keywords:

Discrete coagulation-fragmentation equations,
Smoluchowski equations,
strong fragmentation,
duality arguments,
moments estimates,
regularity.

Mathematics Subject Classification: Primary: 35K57; Secondary: 35B45, 35B65, 82D60.

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