EXISTENCE OF WEAK SOLUTIONS FOR A QUASILINEAR VERSION OF BENNEY EQUATIONS

DOI10.1142/S0219891607001252zbMath1148.35047MaRDI QIDQ3502742

M. S. Figueira, João-Paulo Dias

Publication date: 20 May 2008

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

zbMATH Keywords

compensated compactness

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) First-order nonlinear hyperbolic equations (35L60) Hyperbolic conservation laws (35L65) Initial value problems for first-order hyperbolic systems (35L45)

Related Items (18)

CONVERGENCE OF NUMERICAL SCHEMES FOR SHORT WAVE LONG WAVE INTERACTION EQUATIONS ⋮ Non-existence of global solutions for a quasilinear Benney system ⋮ Existence of local strong solutions for a quasilinear Benney system ⋮ On the motion of the director field of a nematic liquid crystal submitted to a magnetic field and a laser beam ⋮ On Short Wave-Long Wave Interactions in the Relativistic Context ⋮ On a coupled system of a Ginzburg–Landau equation with a quasilinear conservation law ⋮ The linear stability of shock waves for the nonlinear Schrödinger-inviscid Burgers system ⋮ On a quasilinear nonlocal Benney system ⋮ Decay of solutions for a class of nonlinear Schrödinger equations in $ \newcommand{\R}{\mathbb{R}} \R$ and the stability of shock profiles for a quasilinear Benney system ⋮ Global existence and blow-up for the classical solutions of the long-short wave equations with viscosity ⋮ Vanishing viscosity with short wave-long wave interactions for multi-D scalar conservation laws ⋮ Vanishing viscosity with short wave-long wave interactions for systems of conservation laws ⋮ Well-posedness and existence of bound states for a coupled Schrödinger-gKdV system ⋮ A quasilinear system related with the asymptotic equation of the nematic liquid crystal's director field ⋮ On the Cauchy problem describing an electron-phonon interaction ⋮ The initial value problem for some hyperbolic-dispersive system ⋮ A nonlinear model describing a short wave–long wave interaction in a viscoelastic medium ⋮ Linear stability of shock profiles for a quasilinear Benney system in ℝ2 × ℝ+

Cites Work

• Non-classical shocks and kinetic relations: Scalar conservation laws
• A General Theory for Interactions Between Short and Long Waves
• Well-posedness of the cauchy problem for the long wave-short wave resonance equations
• Zero Diffusion-Dispersion Limits for Scalar Conservation Laws

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