Asymptotic behaviour of solutions to a simplified Lifshitz-Slyozov equation

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(lambda, 0) near the largest lambda-values in its support. If c(lambda, 0) has compact support, near whose supremum lambda = a it behaves like (a - lambda)(q), q > -1, then (h) over bar also has compact support, near whose supremum it behaves like (a - lambda)(q+1). If c(lambda, 0) goes to zero exponentially fast as lambda NE arrow a, or if its support is infinite and it decays exponentially fast for large lambda, then (h) over bar(x) is e(-x). If c(lambda, 0) has infinite support and decays for large lambda 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 exist. (C) 1998 Elsevier Science B.V.