For the system
we prove for several classes of initial data c(lambda, 0) that
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.