Thanks a lot Danny. You and Ackbeet are always helping me undertand this vast subject of DE I am just scratching the surface of!

Is it the initial value theorom about the initial condition of $\displaystyle u(x,0) = 0$ ?

This to me would suggest, from having a read through some control engineering notes (that I have dusted down from my attic from many years ago!) that the behaviour of the system as the complex laplace variable, $\displaystyle p$ in our case, hits the limit of infinity the system output will tend to zero- this interprets as high frequency response in control systems.... is this what you were thinking ackbeet?