Asymptotic behaviour of solutions to a simplified Lifshitz-Slyozov equation

Citation
J. Carr et O. Penrose, Asymptotic behaviour of solutions to a simplified Lifshitz-Slyozov equation, PHYSICA D, 124(1-3), 1998, pp. 166-176
Citations number
8
Language
INGLESE
art.tipo
Article
Categorie Soggetti
Physics
Journal title
PHYSICA D
ISSN journal
0167-2789 → ACNP
Volume
124
Issue
1-3
Year of publication
1998
Pages
166 - 176
Database
ISI
SICI code
0167-2789(199812)124:1-3<166:ABOSTA>2.0.ZU;2-H
Abstract
For the system [GRAPHICS] we prove for several classes of initial data c(lambda, 0) that [GRAPHICS] where (h) over bar is a known function determined by the behaviour of c(lam bda, 0) near the largest lambda-values in its support. If c(lambda, 0) has compact support, near whose supremum lambda = a it beha ves like (a - lambda)(q), q > -1, then (h) over bar also has compact suppor t, near whose supremum it behaves like (a - lambda)(q+1). If c(lambda, 0) g oes to zero exponentially fast as lambda NE arrow a, or if its support is i nfinite and it decays exponentially fast for large lambda, then (h) over ba r(x) is e(-x). If c(lambda, 0) has infinite support and decays for large la mbda like a negative power of lambda, then so does (h) over bar. We also give examples of initial data for which the above limit does not ex ist. (C) 1998 Elsevier Science B.V.