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Article Dans Une Revue Kinetic and Related Models Année : 2018

Oscillatory dynamics in Smoluchowski's coagulation equation with diagonal kernel

Résumé

We characterize the long-time behaviour of solutions to Smoluchowski's coagulation equation with a diagonal kernel of homogeneity $\gamma < 1$. Due to the property of the diagonal kernel, the value of a solution depends only on a discrete set of points. As a consequence, the long-time behaviour of solutions is in general periodic, oscillating between different rescaled versions of a self-similar solution. Immediate consequences of our result are a characterization of the set of data for which the solution converges to self-similar form and a uniqueness result for self-similar profiles.
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Dates et versions

hal-01625545 , version 1 (27-10-2017)

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Philippe Laurençot, Barbara Niethammer, Juan J. L. Velazquez. Oscillatory dynamics in Smoluchowski's coagulation equation with diagonal kernel. Kinetic and Related Models , 2018, 11 (4), pp.933-952. ⟨hal-01625545⟩
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