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Method of vanishing viscosity and explicit solution of the Riemann problem for scalar conservation law. (English. Russian original) Zbl 0951.35077

Mosc. Univ. Math. Bull. 54, No. 1, 1-6 (1999); translation from Vestn. Mosk. Univ., Ser. I 1999, No. 1, 3-8 (1999).
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.

MSC:

35L65 Hyperbolic conservation laws
35K55 Nonlinear parabolic equations
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
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