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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 F(u) F(u,) o = us-u, c) Let ut denote the above traveling wave solution of (*) for a with = Compute lim, us and explain your answer.

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Viscous Conservation Law
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