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Gelation in Coagulation and Fragmentation Models

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Abstract:

Rates of decay for the total mass of the solutions to Smoluchovski's equation with homogeneous kernels of degree λ > 1 are proved. That implies that gelation always occurs. Morrey estimates from below and from above on solutions around the gelation time are also obtained which are in agreement with previously known formal results on the profile of solutions at gelling time. The same techniques are applied to the coagulation-fragmentation model for which gelation is established in some particular cases.

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Authors and Affiliations

  1. Departamento de Matemáticas, Universidad del País Vasco, Apartado 644, 48080 Bilbao, Spain.¶E-mail: mtpesmam@lg.ehu.es, , , , , , ES

    M. Escobedo

  2. Laboratoire de Mathématiques Appliquées, Université de Versailles – Saint Quentin, 45 avenue des Etats-Unis, 78035 Versailles, France. E-mail: mischler@math.uvsq.fr, , , , , , FR

    S. Mischler

  3. DMA, UNM 8553, Ecole Normale Supérieure, 45 rue d'Ulm, 75230 Paris cedex 05, France.¶E-mail: perthame@dma.ens.fr, , , , , , FR

    B. Perthame

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  1. M. Escobedo
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  2. S. Mischler
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  3. B. Perthame
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Received: 28 September 2001 / Accepted: 1 April 2002¶Published online: 2 October 2002

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Escobedo, M., Mischler, S. & Perthame, B. Gelation in Coagulation and Fragmentation Models. Commun. Math. Phys. 231, 157–188 (2002). https://doi.org/10.1007/s00220-002-0680-9

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  • DOI: https://doi.org/10.1007/s00220-002-0680-9

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