Abstract :
In this paper we consider an initial-value problem for the nonlinear fourth-order partial
differential equation ut C uux C
ux x x x D 0, 1< x <1, t > 0, where x and t
represent dimensionless distance and time respectively and
is a negative constant.
In particular, we consider the case when the initial data has a discontinuous expansive
step so that u.x; 0/ D u0.> 0/ for x 0 and u.x; 0/ D 0 for x < 0. The method of
matched asymptotic expansions is used to obtain the large-time asymptotic structure of
the solution to this problem which exhibits the formation of an expansion wave. Whilst
most physical applications of this type of equation have
> 0, our calculations show
how it is possible to infer th
