2 7.36, §2 PDE Model

**Figure 2:** Supersonic flow over a membrane.
$\begin{figure}\begin{center} \leavevmode \epsffile{figures/2.ps} \end{center}\end{figure}$

Domain $\bar \Omega$ : $0\le x < \infty, 0\le y < \infty$
Unknown horizontal perturbation velocity
Hyperbolic
Two homogeneous initial conditions
One mixed boundary condition at and a regularity constraint at $y=\infty$
Constant $a = \tan \mu$ , where $\mu$ is the Mach angle.

Try a Laplace transform. The physics and the fact that Laplace transforms like only initial conditions suggest that is the one to be transformed. Variable is our ``time-like'' coordinate.