Resonant Leading Order Geometric Optics Expansions for Quasilinear Hyperbolic Fixed and Free Boundary Problems

DOI10.1080/03605302.2011.594474zbMath1241.35131OpenAlexW1984651586MaRDI QIDQ3106547

Olivier Guès, Jean-François Coulombel, Mark Williams

Publication date: 28 December 2011

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03605302.2011.594474

zbMATH Keywords

highly oscillatory reflecting wavetrainsnoncharacteristic boundariesrigorous error estimatesrigorous nonlinear geometric opticssmall divisors assumption

Mathematics Subject Classification ID

Shocks and singularities for hyperbolic equations (35L67) PDEs in connection with fluid mechanics (35Q35) Initial-boundary value problems for first-order hyperbolic systems (35L50) Geometric optics (78A05) Euler equations (35Q31)

Related Items (8)

Weakly Nonlinear Multiphase Geometric Optics for Hyperbolic Quasilinear Boundary Value Problems: Construction of a Leading Profile ⋮ Transverse instability of high frequency weakly stable quasilinear boundary value problems ⋮ Geometric Optics for Surface Waves in Nonlinear Elasticity ⋮ Unnamed Item ⋮ Nonlinear geometric optics for reflecting uniformly stable pulses ⋮ Hyperbolic boundary problems with large oscillatory coefficients: multiple amplification ⋮ Amplification of pulses in nonlinear geometric optics ⋮ Resonant Leading Term Geometric Optics Expansions with Boundary Layers for Quasilinear Hyperbolic Boundary Problems

Cites Work

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• Asymptotic analysis of contact discontinuities
• The existence of multidimensional shock fronts
• The Block Structure Condition for Symmetric Hyperbolic Systems
• The stability of multidimensional shock fronts
• WAVE TRANSMISSION IN DISPERSIVE MEDIA

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