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On the stability of one-dimensional stationary solutions of hyperbolic systems of differential equations containing points at which one characteristic velocity becomes zero. (English. Russian original) Zbl 0578.35054
J. Appl. Math. Mech. 48(1985), 299-302 (1984); translation from Prikl. Mat. Mekh. 48, 404-419 (1984).
Anfangsrandwertprobleme für nichtlineare hyperbolische Gleichungssysteme auf einem Raumintervall im \({\mathbb{R}}^ 1\) werden betrachtet. Für den Fall, daß eine der charakteristischen Geschwindigkeiten Nullstellen besitzt, wird die Stabilität von zeitunabhängigen Lösungen untersucht.
Reviewer: W.Wendt
MSC:
35L60 First-order nonlinear hyperbolic equations
35L50 Initial-boundary value problems for first-order hyperbolic systems
35B35 Stability in context of PDEs
35B40 Asymptotic behavior of solutions to PDEs
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[1] Kulikovskii, A.G.; Slobodkina, F.A., On the stability of arbitrary steady flows in the neighbourhood of points of transition through the speed of sound, Pmm, Vol.31, No.4, (1967) · Zbl 0257.76061
[2] Kulikovskii, A.G.; Slobodkina, F.A., On the behaviour of small perturbations of one-dimensional steady transonic flows, Pmm, Vol.46, No.6, (1982) · Zbl 0257.76061
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