Consider the viscous conservation law
where a > 0 and F is uniformly convex.
a) Show u solves (*) if u(x,t) = N(I - at) and U is defined implicitly by the formula
8 = =(a) a
where b and c are constants. b) Demonstrate that we can find a traveling wave satisfying
for ut > ur, if and only if
c) Let ut denote the above traveling wave solution of (*) for a with =
Compute lim, us and explain your answer.
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