Attractor and traveling waves of a fluid with nonlinear diffusion and dispersion

DOI10.1016/j.na.2009.12.003zbMath1194.35076OpenAlexW2062172778MaRDI QIDQ847365

Mai Duc Thanh

Publication date: 12 February 2010

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2009.12.003

zbMATH Keywords

Lyapunov stabilityequilibriaisentropic fluidnonclassical shock

Mathematics Subject Classification ID

Attractors (35B41) Dynamics of phase boundaries in solids (74N20) Shock waves and blast waves in fluid mechanics (76L05) Hyperbolic conservation laws (35L65) Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics (76N10) Traveling wave solutions (35C07)

Related Items (9)

Existence of traveling waves in van der Waals fluids with viscosity and capillarity effects ⋮ Existence of traveling waves in elastodynamics with variable viscosity and capillarity ⋮ Exact solutions of a two-fluid model of two-phase compressible flows with gravity ⋮ Existence of traveling waves in compressible Euler equations with viscosity and capillarity ⋮ On traveling waves in viscous-capillary Euler equations with thermal conductivity ⋮ Traveling waves of an elliptic-hyperbolic model of phase transitions via varying viscosity-capillarity ⋮ Remarks on traveling waves and equilibria in fluid dynamics with viscosity, capillarity, and heat conduction ⋮ Existence of traveling waves to any Lax shock satisfying Oleinik’s criterion in conservation laws ⋮ Existence of traveling waves associated with Lax shocks which violate Oleinik’s entropy criterion

Cites Work

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• A vanishing viscosity approach on the dynamics of phase transitions in van der Waals fluids
• The viscosity-capillarity criterion for shocks and phase transitions
• A limiting ``viscosity approach to the Riemann problem for materials exhibiting change of phase
• Global existence of diffusive-dispersive traveling waves for general flux functions
• Traveling waves, Riemann problems and computations of a model of the dynamics of liquid/vapor phase transitions
• Travelling wave solutions of the modified Korteweg-deVries-Burgers equation
• Non-classical shocks and kinetic relations: Scalar conservation laws
• Properties of Rankine-Hugoniot curves for van der Waals fluids.
• Diffusive-dispersive traveling waves and kinetic relations. I: Nonconvex hyperbolic conservation laws
• Admissibility criteria for propagating phase boundaries in a van der Waals fluid
• The Riemann problem for the shallow water equations with discontinuous topography
• The Riemann problem for fluid flows in a nozzle with discontinuous cross-section
• The minimum entropy principle for compressible fluid flows in a nozzle with discontinuous cross-section
• The Riemann Problem for a Nonisentropic Fluid in a Nozzle with Discontinuous Cross-Sectional Area
• Travelling-wave solutions to the Korteweg-de Vries-Burgers equation
• Non-classical Riemann solvers and kinetic relations. II. An hyperbolic–elliptic model of phase-transition dynamics
• Nonclassical Shocks and Kinetic Relations: Strictly Hyperbolic Systems
• Diffusive-dispersive travelling waves and kinetic relations. II A hyperbolic–elliptic model of phase-transition dynamics
• Diffusive–dispersive travelling waves and kinetic relations V. Singular diffusion and nonlinear dispersion
• The Riemann problem for a system of conservation laws of mixed type with a cubic nonlinearity
• NON-MONOTONIC TRAVELING WAVES IN VAN DER WAALS FLUIDS
• Nonclassical Riemann solvers and kinetic relations. I: A nonconvex hyperbolic model of phase transitions

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