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Characteristic decomposition of the \(2\times 2\) quasilinear strictly hyperbolic systems. (English) Zbl 1246.35126

Summary: This paper is devoted to extending the well-known result on reducible equations in R. Courant and K. O. Friedrichs’ book [Supersonic flow and shock waves. Pure Appl. Math. I. New York: Interscience Publ. (1948; Zbl 0041.11302)], that any hyperbolic state adjacent to a constant state must be a simple wave. The authors establish a nice sufficient condition for the existence of characteristic decompositions to the general \(2\times 2\) quasilinear strictly hyperbolic systems. These decompositions allow for a proof that any wave adjacent to a constant state is a simple wave, despite the fact that the coefficients depend on the independent variables. Consequently, as applications, the authors obtain the same results for the pseudo-steady Euler equations.

MSC:

35L60 First-order nonlinear hyperbolic equations
35Q31 Euler equations

Citations:

Zbl 0041.11302
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References:

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