How to solve exactly Riemann problems?
Hello, I want to know how to solve exactly Riemann problems of nonstrictly hyperbolic conservation laws, such as the modified Burgers' equation, u_t+(a(x)u^2)_x=0. Can you give me some advices?Many thanks.

Re: How to solve exactly Riemann problems?
I know the iterate method can solve this problem. Are there any references?

Re: How to solve exactly Riemann problems?
You need to solve the characteristic equations
dt/ds = 1, dx/ds = 2au, du/ds =  a'u^2 with, at s=0, t=0, x=X, u = f(X). 
Re: How to solve exactly Riemann problems?
See the following: Toro, E. F. 1997. Riemann Solvers and Numerical Methods for Fluid Dynamics: A Practical Introduction. Springer New York.
or Godlewski, E. and P.A. Raviart. 1996. Numerical Approximation of Hyperbolic Systems of Conservation Laws. Springer New York. These will tell you everything you need to know. And then some more.  Jarmo 
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