Asymptotic stability of shock profiles and rarefaction waves under periodic perturbations for 1-D convex scalar viscous conservation laws

DOI10.1512/iumj.2021.70.8706zbMath1490.35227arXiv1902.09772OpenAlexW2916138042WikidataQ114846059 ScholiaQ114846059MaRDI QIDQ5025417

Zhouping Xin, Yuan Yuan, Qian Yuan

Publication date: 2 February 2022

Published in: Indiana University Mathematics Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1902.09772

zbMATH Keywords

asymptotic stabilityvanishing viscosityshiftsrarefaction wavesperiodic perturbationsshock profilesviscous scalar conservation laws

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Shocks and singularities for hyperbolic equations (35L67) Hyperbolic conservation laws (35L65) Semilinear parabolic equations (35K58)

Related Items (7)

Periodic Perturbations of a Composite Wave of Two Viscous Shocks for 1-d Full Compressible Navier--Stokes Equations ⋮ Asymptotic stability of planar rarefaction waves under periodic perturbations for 3-d Navier-Stokes equations ⋮ Nonlinear stability of strong traveling waves for a chemotaxis model with logarithmic sensitivity and periodic perturbations ⋮ Nonlinear stability of traveling waves to a parabolic-hyperbolic system modeling chemotaxis with periodic perturbations ⋮ Stability of viscous shock wave under periodic perturbation for compressible Navier–Stokes–Korteweg system ⋮ Time decay rate of solutions toward the viscous shock waves under periodic perturbations for the scalar conservation law with nonlinear viscosity ⋮ Asymptotic stability of the combination of a viscous contact wave with two rarefaction waves for 1-D Navier-Stokes equations under periodic perturbations

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