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The Continuous Coagulation-Fragmentation¶Equations with Diffusion

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Abstract

Existence of global weak solutions to the continuous coagulation-fragmentation equations with diffusion is investigated when the kinetic coefficients satisfy a detailed balance condition or the coagulation coefficient enjoys a monotonicity condition. Our approach relies on weak and strong compactness methods in L 1 in the spirit of the DiPerna-Lions theory for the Boltzmann equation. Under the detailed balance condition the large-time behaviour is also studied.

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Authors and Affiliations

  1. Mathématiques pour l'Industrie et la Physique¶CNRS UMR~5640, Université Paul Sabatier – Toulouse 3¶118 route de Narbonne, 31062 Toulouse cedex 4, France, , , , , , FR

    Philippe Laurençot

  2. Laboratoire de Mathématiques Appliquées¶Université de Versailles – Saint Quentin¶45 avenue des Etats-Unis, 78035 Versailles, France¶DMA, CNRS UMR 8553¶Ecole Normale Supérieure¶45 rue d'Ulm, 75230 Paris cedex 05, France, , , , , , FR

    Stéphane Mischler

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  1. Philippe Laurençot
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  2. Stéphane Mischler
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Accepted October 16, 2001¶Published online March 11, 2002

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Laurençot, P., Mischler, S. The Continuous Coagulation-Fragmentation¶Equations with Diffusion. Arch. Rational Mech. Anal. 162, 45–99 (2002). https://doi.org/10.1007/s002050100186

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  • DOI: https://doi.org/10.1007/s002050100186

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