1 Apply Fourirer transform to the heat equation. discuss the smothness
for t >0. 
2.  discuss the ill-posed case.
3. veryfy rigorously that u(x) = \int G(x,y) f(y) dy solves
        -Lap u = f 
4.use energy principle to show uniqueness of the wave equation
with lower order term.
5. and/or variable coefficient case.

6. find the green function on a quarter plane.