2 7.24, §2 PDE Model

Figure 2: Viscous flow next to a moving plate

• Semi-infinite domain $\bar \Omega$: $0\le x < \infty$
• Unknown vertical velocity $u=u(x,t)$
• Parabolic
• One homogeneous initial condition
• One Neumann boundary condition at $x=0$ and a regularity constraint at $x=\infty$
• Constant kinematic viscosity $\kappa$

Try a Laplace transform in $t$.