A rigorous derivation of Smoluchowski's equation in the moderate limit

• Verfasst von: Großkinsky, Stefan [VerfasserIn]
• Verfasst von: Klingenberg, Christian [VerfasserIn]
• Verfasst von: Oelschläger, Karl [VerfasserIn]
• Titel: A rigorous derivation of Smoluchowski's equation in the moderate limit
• Verf.angabe: S. Großkinsky, C. Klingenberg, K. Oelschläger
• Jahr des Originals: 2004
• Umfang: 29 S.
• Fussnoten: Published online: 16 Aug 2006 ; Gesehen am 13.06.2018
• Titel Quelle: Enthalten in: Stochastic analysis and applications
• Jahr Quelle: 2006
• Band/Heft Quelle: 22(2004), 1, S. 113-141
• ISSN Quelle: 1532-9356
• DOI: doi:10.1081/SAP-120028026
• Datenträger: Online-Ressource
• Sprache: eng
• K10plus-PPN: 1576329585

Abstract

Smoluchowski's equation is a macroscopic description of a many particle system with coagulation and shattering interactions. We give a microscopic model of the system from which we derive this equation rigorously. Provided the existence of a unique and sufficiently regular solution of Smoluchowski's equation, we prove the law of large numbers for the empirical processes. In contrast to previous derivations we assume a moderate scaling of the particle interaction, enabling us to estimate the critical fluctuation terms by using martingale inequalities. This approach can be justified in the regime of high temperatures and particle densities, which is of special interest in astrophysical studies and where previous derivations do not apply.