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Bianchini, S., Hanouzet, B. and Natalini, R. (2007) Asymptotic Behavior of Smooth Solutions for Partially Dissipative Hyperbolic Systems with a Convex Entropy. Communications on Pure and Applied Mathematics, 60, 1559-1622.
https://doi.org/10.1002/cpa.20195

has been cited by the following article:

• TITLE: The Decay Property of Cauchy Problem for Viscoelastic Hyperbolic Systems with Dissipation

  AUTHORS: Jing Hu

  KEYWORDS: Viscoelastic Systems, Regularity-Loss, Optimal Decay Estimates, -- Estimates

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.13 No.4, April 8, 2025

  ABSTRACT: This paper investigates the decay properties of solutions to the Cauchy problem for viscoelastic nonlinear hyperbolic dissipative systems on ℝ 3 . Due to the weak dissipation of the system, the decay estimate of solutions exhibits a loss of regularity, implying that a higher regularity of initial data is required for optimal decay rates compared to the global existence. The aim is to reduce the initial regularity to the lowest possible level to achieve the optimal decay rate. Based on the global existence, we employ energy methods, L p - L q - L r estimates, and harmonic analysis tools to obtain the optimal decay result of solutions.