Asymptotic Stability of Shock Waves and Rarefaction Waves under Periodic Perturbations for 1-D Convex Scalar Conservation Laws

DOI10.1137/18M1192883zbMath1445.35249arXiv1809.09308WikidataQ114847153 ScholiaQ114847153MaRDI QIDQ5231331

Zhouping Xin, Qian Yuan, Yuan Yuan

Publication date: 26 August 2019

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1809.09308

zbMATH Keywords

conservation lawsshock wavesrarefaction wavesperiodic perturbations

Mathematics Subject Classification ID

Shocks and singularities for hyperbolic equations (35L67) Hyperbolic conservation laws (35L65) Initial value problems for first-order hyperbolic equations (35L03)

Related Items (10)

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 ⋮ Planar Viscous Shocks with Periodic Perturbations for Scalar Multidimensional Viscous Conservation Laws ⋮ 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 ⋮ Stability of large-amplitude viscous shock under periodic perturbation for 1-d isentropic Navier-Stokes equations ⋮ On Riemann solutions under different initial periodic perturbations at two infinities for 1-d scalar convex conservation laws ⋮ Asymptotic Stability of Shock Waves and Rarefaction Waves under Periodic Perturbations for 1-D Convex Scalar Conservation Laws ⋮ Asymptotic stability of the combination of a viscous contact wave with two rarefaction waves for 1-D Navier-Stokes equations under periodic perturbations

Cites Work

• Large time behavior of periodic solutions of hyperbolic systems of conservation laws
• Hyperbolic systems of conservation laws II
• Invariants and Asymptotic Behavior of Solutions of a Conservation Law
• Asymptotic Stability of Shock Waves and Rarefaction Waves under Periodic Perturbations for 1-D Convex Scalar Conservation Laws
• Decay of solutions of systems of nonlinear hyperbolic conservation laws
• The partial differential equation u_t + uu_x = μ_xx
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