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A theory for spontaneous Mach-stem formation in reacting shock fronts. II: Steady-wave bifurcations and the evidence for breakdown. (English) Zbl 0584.76075
[For part I see the authors, SIAM J. Appl. Math. 43, 1310-1334 (1983; Zbl 0544.76135)]
This paper continues earlier work of the authors on a theory for spontaneous Mach-stem formation. Shock formation in smooth solutions of the scalar integrodifferential conservation law from paper I is demonstrated through detailed numerical experiments - this completes the basic argument from paper I. The steady-state bifurcation of planar detonation waves into ”shallow-angle” reactive Mach stem structures is analyzed. The conclusions of this analysis agree with those predicted through the time-dependent asymptotics in paper I and provide a completely independent confirmation of that theory.

MSC:
76L05 Shock waves and blast waves in fluid mechanics
80A99 Thermodynamics and heat transfer
76E99 Hydrodynamic stability
76M99 Basic methods in fluid mechanics
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References:
[1] Fickett, Detonation (1979)
[2] Courant, Supersonic Flow and Shock Waves (1948)
[3] Majda, A theory for spontaneous Mach stem formation in reacting shock fronts, I: The basic perturbation analysis, SIAM J. Appl. Math. 43 (6) pp 1310– (1983) · Zbl 0544.76135 · doi:10.1137/0143088
[4] Sattinger, Topics in Stability and Bifurcation Theory (1973) · doi:10.1007/BFb0060079
[5] Whitham, Linear and Nonlinear Waves (1974)
[7] Lax, Weak solutions of nonlinear hyperbolic equations and their numerical computation, Comm. Pure Appl. Math. 7 pp 159– (1954) · Zbl 0055.19404 · doi:10.1002/cpa.3160070112
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