The Signaling Problem in Nonlinear Hyperbolic Wave Theory

DOI10.1002/sapm1991854343zbMath0757.35041OpenAlexW2379889753MaRDI QIDQ3989558

Yuanping He, T. Bryant Moodie

Publication date: 28 June 1992

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

Full work available at URL: https://doi.org/10.1002/sapm1991854343

zbMATH Keywords

eikonal transformationweakly nonlinear wave solutionsinterior shockslocal linear degeneracy at the leading wavefrontshock initiation positionsmall-amplitude, high-frequency boundary disturbances

Mathematics Subject Classification ID

Shocks and singularities for hyperbolic equations (35L67) Wave equation (35L05) First-order nonlinear hyperbolic equations (35L60) Asymptotic expansions of solutions to PDEs (35C20)

Related Items (9)

Scalar Conservation Laws and Spatially Dependent Flux Functions ⋮ Two‐Wave Interactions for Hyperbolic Signaling Problems and the Application to Supersonic Gas Dynamics ⋮ Asymptotic Analysis of a Hyperbolic Mixed Problem in One‐Dimensional Viscoelasticity ⋮ Asymptotic Analysis of a Nonlinear Problem in Thermoelasticity ⋮ Two-Wave Interactions for Weakly Nonlinear Hyperbolic Waves ⋮ Gravity Currents Produced by Sudden Release of a Fixed Volume of Heavy Fluid ⋮ Wavefront expansions and nonlinear hyperbolic waves ⋮ Internal waves, turbulence and mixing in stratified flows: a report on Euromech Colloquium 339 ⋮ Shock Wave Tracking for Hyperbolic Systems Exhibiting Local Linear Degeneracy

Cites Work

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• Reductive perturbation method for quasi one-dimensional nonlinear wave propagation. I
• Reductive Perturbation Method for Nonlinear Wave Propagation in Inhomogeneous Media. II
• Reductive Perturbation Method for Nonlinear Wave Propagation in Inhomogeneous Media. III
• Weakly nonlinear high frequency waves
• Resonantly Interacting Weakly Nonlinear Hyperbolic Waves. I. A Single Space Variable
• Resonantly Interacting, Weakly Nonlinear Hyperbolic Waves. II. Several Space Variables
• Nonlinear waves and shock calculations for hyperelastic fluid-filled tubes

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