\(L^p\)-decay rates of planar viscous rarefaction wave for scalar conservation law with degenerate viscosity in \(n\)-dimensions

DOI10.1016/J.NA.2008.02.097zbMath1154.35393OpenAlexW2032462481MaRDI QIDQ1001871

Changjiang Zhu, Yan-Hong Liu

Publication date: 19 February 2009

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.2008.02.097

zbMATH Keywords

decay ratesdegenerate viscosityplanar viscous rarefaction wave\(L^p\)-energy method\(L^{1}\)-estimate

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Degenerate parabolic equations (35K65) Hyperbolic conservation laws (35L65) A priori estimates in context of PDEs (35B45)

Related Items (2)

Two‐dimensional fractal Burgers equation with step‐like initial conditions ⋮ \(L^p\)-decay rates of planar viscous rarefaction wave for scalar conservation law with degenerate viscosity in \(n\)-dimensions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Existence of weak solutions for a degenerate generalized Burgers equation with large initial data
• Compressible fluid flow and systems of conservation laws in several space variables
• Asymptotic stability of rarefraction waves for 2\(\times 2\) viscous hyperbolic conservation laws - the two-modes case
• \(L^p\)-decay rates of planar viscous rarefaction wave for scalar conservation law with degenerate viscosity in \(n\)-dimensions
• Rarefactions and large time behavior for parabolic equations and monotone schemes
• Large time behavior for convection-diffusion equations in \(\mathbb{R}{} ^ N\)
• Global stability of the rarefaction wave of a one-dimensional model system for compressible viscous gas
• Asymptotic stability of stationary waves for two-dimensional viscous conservation laws in half plane
• Nonlinear stability of strong planar rarefaction waves for the relaxation approximation of conservation laws in several space dimensions
• Asymptotic behavior of solutions for \(p\)-system with relaxation
• Asymptotic stabilitiy of rarefaction wave for generalized Burgers equation
• A note on the stability of the rarefaction wave of the Burgers equation
• Decay rates of strong planar rarefaction waves to scalar conservation laws with degenerate viscosity in several space dimensions
• Asymptotic solutions of model equations in nonlinear acoustics
• Behaviors of Solutions for the Burgers Equation with Boundary corresponding to Rarefaction Waves
• Asymptotic Decay toward the Rarefaction Waves of Solutions for Viscous Conservation Laws in a One-Dimensional Half Space
• L^p ENERGY METHOD FOR MULTI-DIMENSIONAL VISCOUS CONSERVATION LAWS AND APPLICATION TO THE STABILITY OF PLANAR WAVES
• Asymptotics toward the planar rarefaction wave for viscous conservation law in two space dimensions
• ASYMPTOTIC DECAY TOWARD THE PLANAR RAREFACTION WAVES OF SOLUTIONS FOR VISCOUS CONSERVATION LAWS IN SEVERAL SPACE DIMENSIONS
• Behavior of the solutions of the Cauchy problem for certain quasilinear equations for unbounded increase of the time
• Asymptotic Stability of Planar Rarefaction Waves for Viscous Conservation Laws in Several Dimensions

This page was built for publication: \(L^p\)-decay rates of planar viscous rarefaction wave for scalar conservation law with degenerate viscosity in \(n\)-dimensions