On the Decay of Solutions of the Linearized Equations of Conservation Equations with Viscosity and Relaxation

• Joaquín Delgado ^[1] ; Patricia Saavedra ^[1]
  1. [1] Universidad Autónoma Metropolitana–Iztapalapa
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 21, Nº 4, 2022
• Idioma: inglés
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• Resumen

  • In this paper we study the stability of homogeneous states in a continuous one spatial variable of conservation equations in Lagrangian coordinates, including terms of dissipation and relaxation. Local existence is proved applying Kawashima’s theorem for hyperbolic-parabolic systems [7]. We establish that when the subcharactertistic condition is satisfied, the structure of the system is not of regularity-loss type, but of the standard type, even though the linear term associated with relaxation is not symmetric nor positive semidefinite.