TY - JOUR

T1 - Asymptotic behaviour of solutions to a simplified Lifshitz-Slyozov equation

AU - Carr, J.

AU - Penrose, O.

PY - 1998

Y1 - 1998

N2 - For the system matrix presented we prove for several classes of initial data c(?, 0) that matrix presented where h¯ is a known function determined by the behaviour of c(?, 0) near the largest ?-values in its support. If c(?, 0) has compact support, near whose supremum ? = a it behaves like (a - ?)q, q > -1, then h¯ also has compact support, near whose supremum it behaves like (a - ?)q+1. If c(?, 0) goes to zero exponentially fast as ? ? a, or if its support is infinite and it decays exponentially fast for large ?, then h¯(x) is e-x. If c(?, 0) has infinite support and decays for large ? like a negative power of ?, then so does h¯. We also give examples of initial data for which the above limit does not exist. © 1998 Elsevier Science B.V.

AB - For the system matrix presented we prove for several classes of initial data c(?, 0) that matrix presented where h¯ is a known function determined by the behaviour of c(?, 0) near the largest ?-values in its support. If c(?, 0) has compact support, near whose supremum ? = a it behaves like (a - ?)q, q > -1, then h¯ also has compact support, near whose supremum it behaves like (a - ?)q+1. If c(?, 0) goes to zero exponentially fast as ? ? a, or if its support is infinite and it decays exponentially fast for large ?, then h¯(x) is e-x. If c(?, 0) has infinite support and decays for large ? like a negative power of ?, then so does h¯. We also give examples of initial data for which the above limit does not exist. © 1998 Elsevier Science B.V.

UR - http://www.scopus.com/inward/record.url?scp=0001540136&partnerID=8YFLogxK

U2 - 10.1016/S0167-2789(98)00188-2

DO - 10.1016/S0167-2789(98)00188-2

M3 - Article

SN - 0167-2789

VL - 124

SP - 166

EP - 176

JO - Physica D: Nonlinear Phenomena

JF - Physica D: Nonlinear Phenomena

IS - 1-3

ER -