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<p>We study wave propagation in viscoelastic materials based on a system of viscous conservation laws derived from the viscoelastic dynamic system with fading memory. In this model, the stress is a non-convex function of the strain, in contrast to the Euler equations of gas dynamics, which possess a convex constitutive relation. The non-convex nature of the viscoelastic model permits composite wave patterns within the same characteristic family, which greatly complicates the analysis of wave behavior. To address this challenge, we establish a new weighted Poincaré-type inequality for the study of the nonlinear stability of such composite wave patterns.</p>

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Asymptotic Stability of the Composite Wave of Rarefaction Wave and Contact Wave to Nonlinear Viscoelasticity Model with Non-convex Flux

  • 期刊论文

  • 发表日期：

    2026年5月26日

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  • Zhenhua Guo,
  • Meichen Hou,
  • Guiqin Qiu,
  • Lingda Xu

摘要

We study wave propagation in viscoelastic materials based on a system of viscous conservation laws derived from the viscoelastic dynamic system with fading memory. In this model, the stress is a non-convex function of the strain, in contrast to the Euler equations of gas dynamics, which possess a convex constitutive relation. The non-convex nature of the viscoelastic model permits composite wave patterns within the same characteristic family, which greatly complicates the analysis of wave behavior. To address this challenge, we establish a new weighted Poincaré-type inequality for the study of the nonlinear stability of such composite wave patterns.