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.