Vanishing viscosity with short wave-long wave interactions for multi-D scalar conservation laws

DOI10.1016/j.jde.2011.05.007zbMath1227.35204OpenAlexW2085750789MaRDI QIDQ549226

Hermano Frid, M. S. Figueira, João-Paulo Dias

Publication date: 7 July 2011

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2011.05.007

zbMATH Keywords

local existenceglobal existencesmall interaction parameter

Mathematics Subject Classification ID

Singular perturbations in context of PDEs (35B25) Hyperbolic conservation laws (35L65) PDEs in connection with quantum mechanics (35Q40) Initial value problems for first-order hyperbolic systems (35L45)

Related Items (3)

Analytical solutions for nonlinear long-short wave interaction systems with highly complex structure ⋮ Well-posedness and existence of bound states for a coupled Schrödinger-gKdV system ⋮ Linear stability of shock profiles for a quasilinear Benney system in ℝ2 × ℝ+

Cites Work

• The Cauchy problem for the nonlinear Schrödinger equation in \(H^ 1\)
• Vanishing viscosity with short wave-long wave interactions for systems of conservation laws
• The global Cauchy problem for the nonlinear Schrödinger equation revisited
• Existence of solutions for Schrödinger evolution equations
• Restrictions of Fourier transforms to quadratic surfaces and decay of solutions of wave equations
• Interaction equations for short and long dispersive waves
• Measure-valued solutions to conservation laws
• EXISTENCE OF WEAK SOLUTIONS FOR A QUASILINEAR VERSION OF BENNEY EQUATIONS
• A General Theory for Interactions Between Short and Long Waves
• Endpoint Strichartz estimates
• Well-posedness of the cauchy problem for the long wave-short wave resonance equations
• Weak solvability and well-posedness of a coupled Schrödinger-Korteweg de Vries equation for capillary-gravity wave interactions
• FIRST ORDER QUASILINEAR EQUATIONS IN SEVERAL INDEPENDENT VARIABLES
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Vanishing viscosity with short wave-long wave interactions for multi-D scalar conservation laws