Method of vanishing viscosity and explicit solution of the Riemann problem for scalar conservation law (Q1584100)

The paper addresses the Riemann problem on the decay of arbitrary discontinuity for scalar quasilinear conservation law with one spatial variable \[ u_t + f(u)_x = 0, \qquad u\big|_{t=0} = \begin{cases} u^-, & x<0\\ u^+, &x>0\end{cases}. \] The author derives a formula for the solution of this problem. For the corresponding parabolic problem the existence and uniqueness of the automodel solution is proved.