[SOLVED] Amath 569 homework assignment 1

1. Solve the PDE:
,
subject to the initial condition:2. Consider the initial value problem in infinite domain:
(a) Find where and when a shock first forms.
(b) Solve the problem and sketch or plot the solution before when a shock first forms.
(c) Find the shock speed using the Rankine-Hugoniot condition.
(d) Solve the problem and sketch or plot the solution after the shock has formed.3. Solve the PDE:
,
subject to the initial condition:
Where in the x-t plane is the solution valid?