Existence of traveling waves in elastodynamics with variable viscosity and capillarity

DOI10.1016/J.NONRWA.2010.06.010zbMath1202.35051OpenAlexW2034717226MaRDI QIDQ611234

Mai Duc Thanh

Publication date: 14 December 2010

Published in: Nonlinear Analysis. Real World Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.nonrwa.2010.06.010

zbMATH Keywords

Lyapunov functionattraction domainLax shock inequalities

Mathematics Subject Classification ID

Shocks and singularities for hyperbolic equations (35L67) Hyperbolic conservation laws (35L65) Traveling wave solutions (35C07)

Related Items (8)

Existence of traveling waves in van der Waals fluids with viscosity and capillarity effects ⋮ Existence of standing and traveling waves in quantum hydrodynamics with viscosity ⋮ 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

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
• Attractor and traveling waves of a fluid with nonlinear diffusion and dispersion
• 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
• Diffusive-dispersive travelling waves and kinetic relations. II A hyperbolic–elliptic model of phase-transition dynamics
• 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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