A Theory for Spontaneous Mach-Stem Formation in Reacting Shock Fronts. II. Steady-Wave Bifurcations and the Evidence for Breakdown

DOI10.1002/sapm1984712117zbMath0584.76075OpenAlexW210212762MaRDI QIDQ3707667

Rodolfo Ruben Rosales, Andrew J. Majda

Publication date: 1984

Published in: Studies in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/sapm1984712117

zbMATH Keywords

smooth solutionssteady-state bifurcationShock formationplanar detonation wavesscalar integrodifferential conservation lawshallow-angle reactive Mach stem structuresspontaneous Mach-stem formationtime-dependent asymptotics

Mathematics Subject Classification ID

Shock waves and blast waves in fluid mechanics (76L05) Thermodynamics and heat transfer (80A99) Hydrodynamic stability (76E99) Basic methods in fluid mechanics (76M99)

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Nonlinear development of instabilities in supersonic vortex sheets. I. The basic kink modes ⋮ Stability of surfaces of strong discontinuity in gases ⋮ Transverse instability of high frequency weakly stable quasilinear boundary value problems ⋮ Multi‐dimensional shock fronts for second order wave equations ⋮ On the Mach stem configuration with shallow angle ⋮ The interaction of nonlinear hyperbolic waves ⋮ Resonantly Interacting, Weakly Nonlinear Hyperbolic Waves. II. Several Space Variables ⋮ Nonlinear kink modes for supersonic vortex sheets ⋮ The refined inviscid stability condition and cellular instability of viscous shock waves ⋮ The Riemann problem for fluid flow of real materials ⋮ Resonantly Interacting Weakly Nonlinear Hyperbolic Waves. I. A Single Space Variable

Cites Work

• A Theory for Spontaneous Mach Stem Formation in Reacting Shock Fronts, I. The Basic Perturbation Analysis
• Weak solutions of nonlinear hyperbolic equations and their numerical computation