Characterization of Dissipative Structures for First-Order Symmetric Hyperbolic System with General Relaxation

Abstract

In this paper, we study the dissipative structure of first-order linear symmetric hyperbolic system with general relaxation and provide the algebraic characterization for the uniform dissipativity up to order 1. Our result extends the classical Shizuta–Kawashima condition for the case of symmetric relaxation, with a full generality and optimality.

Keywords

• symmetric hyperbolic system with relaxation
• dissipative structure
• time decay with regularity-loss