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Glimm’s scheme for systems with almost-planar interactions. (English) Zbl 0746.35022
The Cauchy problem for a strictly-hyperbolic system of nonlinear conservation laws for which each field is either genuinely nonlinear or linearly degenerate is considered. The condition \([R_ i(u),R_ j(u)]=0\), \(\forall i,j,u\), where \(R_ j=r_ j\nabla u\) of Glimm’s existence theorem is relaxed to \(C^ k_{ij}({\tilde{u}})=0\), \(\forall i,j,k\), where \([R_ i(u),R_ j(u)]=\sum_ k C^ k_{ij}(u)R_ k(u)\). The proved existence theorem is examined under the above mentioned requirement for the Euler equations.
Reviewer: K.Zlateva (Russe)

35L65 Hyperbolic conservation laws
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35L80 Degenerate hyperbolic equations
65M99 Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
65N99 Numerical methods for partial differential equations, boundary value problems
Full Text: DOI
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