The Mach stem equation and amplification in strongly nonlinear geometric optics

DOI10.1353/AJM.2017.0026zbMath1383.35221arXiv1501.02793OpenAlexW1904393121MaRDI QIDQ5349329

Mark Williams, Jean-François Coulombel

Publication date: 24 August 2017

Published in: American Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1501.02793

zbMATH Keywords

approximate solutionsgeometric opticsfirst order hyperbolic equationWKB cascadeMach stem equationquasilinear weak well-posedness

Mathematics Subject Classification ID

PDEs in connection with optics and electromagnetic theory (35Q60) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30) Geometric optics (78A05) Initial-boundary value problems for first-order hyperbolic equations (35L04) Initial-boundary value problems for nonlinear first-order PDEs (35F31)

Related Items (7)

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 ⋮ On the Mach stem configuration with shallow angle ⋮ Weakly stable hyperbolic boundary problems with large oscillatory coefficients: Simple cascades ⋮ Hyperbolic boundary problems with large oscillatory coefficients: multiple amplification ⋮ WKB expansions for weakly well-posed hyperbolic boundary value problems in a strip: Time depending loss of derivatives

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