A nonlinear model describing a short wave–long wave interaction in a viscoelastic medium

DOI10.1090/S0033-569X-2012-01298-4zbMath1275.35082arXiv1202.1235OpenAlexW1971318536MaRDI QIDQ2850024

João-Paulo Dias, Paulo Amorim

Publication date: 20 September 2013

Published in: Quarterly of Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1202.1235

zbMATH Keywords

polymersplasmasquasilinear viscoelasticity system

Mathematics Subject Classification ID

NLS equations (nonlinear Schrödinger equations) (35Q55) Nonlinear constitutive equations for materials with memory (74D10) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) Initial value problems for systems of nonlinear higher-order PDEs (35G55)

Related Items

The linear stability of shock waves for the nonlinear Schrödinger-inviscid Burgers system

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the Cauchy problem describing an electron-phonon interaction
• Existence of local strong solutions for a quasilinear Benney system
• Vanishing viscosity with short wave-long wave interactions for systems of conservation laws
• Convergence of semi-discrete approximations of Benney equations
• Convergence of approximate solutions to conservation laws
• Stability of the solitons for the one-dimensional Zakharov-Rubenchik equation
• On the existence of weak solutions to the Cauchy problem for a class of quasilinear hyperbolic equations with a source term
• A system of hyperbolic conservation laws with frictional damping
• CONVERGENCE OF NUMERICAL SCHEMES FOR SHORT WAVE LONG WAVE INTERACTION EQUATIONS
• Short Wave–Long Wave Interactions for Compressible Navier–Stokes Equations
• EXISTENCE OF WEAK SOLUTIONS FOR A QUASILINEAR VERSION OF BENNEY EQUATIONS
• Weak solutions for a nonlinear system in viscoelasticity
• A model for one-dimensional, nonlinear viscoelasticity
• A General Theory for Interactions Between Short and Long Waves
• Well-posedness of the cauchy problem for the long wave-short wave resonance equations
• A remark on the existence of global BV solutions for a nonlinear hyperbolic wave equation