On the System of Hamilton–Jacobi and Transport Equations Arising in Geometrical Optics

DOI10.1081/PDE-120021187zbMath1029.78002MaRDI QIDQ4707067

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Publication date: 9 June 2003

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

zbMATH Keywords

viscosity solutiontransport equationeikonal equationmeasure solutionFilippov characteristicshigh frequency characteristics

Mathematics Subject Classification ID

Shocks and singularities for hyperbolic equations (35L67) PDEs in connection with optics and electromagnetic theory (35Q60) Initial value problems for nonlinear first-order PDEs (35F25) Waves and radiation in optics and electromagnetic theory (78A40) Geometric optics (78A05)

Related Items (5)

Weak Solutions for First Order Mean Field Games with Local Coupling ⋮ On numerical approximation of the Hamilton-Jacobi-transport system arising in high frequency approximations ⋮ A one-dimensional inviscid and compressible fluid in a harmonic potential well ⋮ On the Hamilton-Jacobi equation for a harmonic oscillator ⋮ Semiconcavity estimates for viscous Hamilton-Jacobi equations

Cites Work

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• Big ray tracing: Multivalued travel time field computation using viscosity solutions of the eikonal equation
• Existence of viscosity solutions of Hamilton-Jacobi equations
• Numerical solution of the high frequency asymptotic expansion for the scalar wave equation
• Formation of singularities for viscosity solutions of hamilton—jacobi equations in higher dimensions
• Two approximations of solutions of Hamilton-Jacobi equations
• User’s guide to viscosity solutions of second order partial differential equations
• One-dimensional transport equations with discontinuous coefficients
• Measure solutions to the linear multi-dimensional transport equation with non-smooth coefficients
• Multivalued solutions to the eikonal equation in stratified media
• Direct computation of multivalued phase space solutions for Hamilton-Jacobi equations
• Generalized one-sided estimates for solutions of Hamilton-Jacobi equations and applications
• COMPUTATION OF HIGH FREQUENCY FIELDS NEAR CAUSTICS
• Convergence of SPH Method for Scalar Nonlinear Conservation Laws
• Differential equations with discontinuous right-hand side
• GENERALIZED SOLUTIONS OF NONLINEAR FIRST ORDER EQUATIONS WITH SEVERAL INDEPENDENT VARIABLES. II

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