Due at the beginning of class, Tuesday Nov 16.


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1. The method of searching for similarity solutions
by looking for a scaling-invariance can work for 
NON-linear equations too.
Consider the nonlinear Boltzmann diffusion equation
ut = ( u ux )x
with the same additional conditions that we applied 
to the linear heat (or diffusion) equation.
Use the method you saw in class (or in F&M) to
find that there is similarity solution involving a
function U(&xi) satisfying  3 U U' + &xi U = 0.

2. Extra credit. Can you find a piecewise differentiable
U that satisfies the above ODE and the normalization
condition? If so, write the corresponding solution, u(x,t)
of the PDE and use Maple to make an animation of it for x
and t in some appropriate ranges.