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<p>In this paper, we study a hyperbolic model for nonlinear viscoelasticity in one-dimensional space from the point of view of Lie symmetries. The study leads to a classification of all functional forms of the constitutive relations that admit nontrivial symmetry under physical constraints. We then use the obtained symmetries to derive reductions and some exact solutions. Finally, we apply the direct method of Bluman-Anco to construct the local conservation laws associated with the system.</p>

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A Lie Group Approach to a Viscoelasticity Model

  • 期刊论文

  • 发表日期：

    2026年4月27日

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  • Alessandra Rizzo,
  • Emanuele Sgroi

摘要

In this paper, we study a hyperbolic model for nonlinear viscoelasticity in one-dimensional space from the point of view of Lie symmetries. The study leads to a classification of all functional forms of the constitutive relations that admit nontrivial symmetry under physical constraints. We then use the obtained symmetries to derive reductions and some exact solutions. Finally, we apply the direct method of Bluman-Anco to construct the local conservation laws associated with the system.