×

The generalized Riemann problem for first order quasilinear hyperbolic systems of conservation laws. I. (English) Zbl 1178.35245

The authors consider the first order quasilinear hyperbolic system of conservation laws with one spatial variable. The initial data are piecewise continuous, i.e. the generalized Riemann problem is considered. It is shown that for sufficiently smooth coefficients this problem has a unique piecewise smooth local solution, and the structure of the solution is similar to the similarity solution of the Riemann problem in the neighborhood of the origin.

MSC:

35L65 Hyperbolic conservation laws
35L60 First-order nonlinear hyperbolic equations
35L45 Initial value problems for first-order hyperbolic systems
35L67 Shocks and singularities for hyperbolic equations
PDFBibTeX XMLCite
Full Text: DOI