A Numerical Study on Large-Time Asymptotics of the Lifshitz–Slyozov System

Authors:
J. A. Carrillo;T. Goudon
Affiliations:
Departament de Matemátiques–ICREA, Universitát Autónoma de Barcelona, E-08193 Bellaterra, Spain. carrillo@ugr.es;Université des Sciences et Technologies Lille 1, Cité Scientifique, F-59655 Villeneuve d'Ascq cedex, France. Thierry.Goudon@univ-lille1.fr
Venue:
Journal of Scientific Computing
Year:
2004

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Abstract

We numerically investigate the long time behavior of solutions of the Lifshitz–Slyozov system. We propose a numerical scheme in which the numerical dissipation is controlled in such a way that the results for large time are meaningful. In this respect, we find the long time behavior to crucially depend on the distribution of largest aggregates present in the solution. This fact proved, in some particular cases in (23), was difficult to obtain with previous numerical schemes in the engineering literature leading to wrong statements. We propose a numerical scheme in which we can observe and quantify the equilibration rates towards the right asymptotic profile. Moreover, this system appears to be a very interesting test problem for any anti dissipative scheme for conservation laws.