Skip to content
DraconiticResearch
Search Sources API
184,584 studies31 sourcesUpdated 10 min ago
PreprintarXiv licencearXiv

Decay Rate toward the Rarefaction Wave and the Viscous Contact Wave for Jin--Xin Relaxation Model

  • Mutong He
  • Feimin Huang
  • Tianyi Wang
  • Lingda Xu
Open at sourcePDFDOICite

Abstract

This paper establishes the time-decay rates toward the rarefaction wave and the viscous contact wave for the one-dimensional Jin--Xin relaxation system under the L1 integrability condition of the initial perturbation. In the case of a strictly convex flux, we employ a decomposition method to derive a logarithmic L1 estimate related to a conjecture proposed by Liu\cite{liu2001lp}. Furthermore, a time-weighted L2 method yields the optimal decay rate toward the rarefaction wave. Regarding the case where the flux is partially linearly degenerate, by employing a similar L1 estimate and time-weighted L2 method, along with a refined estimate of the nonlinear wave interactions, we obtain the corresponding decay rate toward the composite wave. The decay estimates are obtained without smallness assumptions on the initial perturbations or the wave strength.

Related

  1. Global stability of superposition of viscous contact wave and rarefaction waves for compressible Navier-Stokes system with temperature-dependent transport coefficients and large data
    Hongyu Wang, Rong Zhang
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv
  2. Asymptotic Stability and Lp Time-Decay Rates of Rarefaction Waves for Systems of Viscous Conservation Laws
    Mutong He, Feimin Huang, Lingjun Liu +1
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv
  3. Optimal Decay Exponents for Fractional Burgers Rarefaction Waves
    Tuoc Phan, Atanas G. Stefanov
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv
  4. Time-Decay Rates toward Rarefaction Waves for the One-Dimensional Isentropic Compressible Navier--Stokes Equations
    Mutong He, Feimin Huang, Lingjun Liu +1
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv
  5. Convergence Rate toward Rarefaction Wave under Periodic Perturbation for Generalized Korteweg-de Vries-Burgers equation
    Lin Chang, Yuling Xu
    arXivPreprintCC BY 4.0Full textAnalysis & PDEsarXiv

Cite

BibTeXRIS
BibTeX
@misc{he2026decay,
  title = {{Decay Rate toward the Rarefaction Wave and the Viscous Contact Wave for Jin--Xin Relaxation Model}},
  author = {Mutong He and Feimin Huang and Tianyi Wang and Lingda Xu},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.00969},
  eprint = {2611.00969},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.00969},
}
RIS
TY  - UNPB
TI  - Decay Rate toward the Rarefaction Wave and the Viscous Contact Wave for Jin--Xin Relaxation Model
AU  - Mutong He
AU  - Feimin Huang
AU  - Tianyi Wang
AU  - Lingda Xu
PY  - 2026
DA  - 2026/11/01
PB  - arXiv
DO  - 10.48550/arxiv.2611.00969
UR  - https://arxiv.org/abs/2611.00969
AB  - This paper establishes the time-decay rates toward the rarefaction wave and the viscous contact wave for the one-dimensional Jin--Xin relaxation system under the L^1 integrability condition of the initial perturbation. In the case of a strictly convex flux, we employ a decomposition method to derive a logarithmic L^1 estimate related to a conjecture proposed by Liu\cite{liu2001lp}. Furthermore, a time-weighted L^2 method yields the optimal decay rate toward the rarefaction wave. Regarding the case where the flux is partially linearly degenerate, by employing a similar L^1 estimate and time-weighted L^2 method, along with a refined estimate of the nonlinear wave interactions, we obtain the corresponding decay rate toward the composite wave. The decay estimates are obtained without smallness assumptions on the initial perturbations or the wave strength.
ER  -