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

Joaquín Delgado, Patricia Saavedra

• 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.