Basic Aspects of Hyperbolic Relaxation Systems

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Entropy and Global Existence for Hyperbolic Balance Laws (2004, methodology): “Furthermore, it was shown in [22] that many systems of balance laws from mathematical physics and numerics have the form (1.”
Global Existence of Smooth Solutions for Partially Dissipative Hyperbolic Systems with a Convex Entropy (2003, background): “Remark 2. The dissipative-entropy condition is strictly related to various stability conditions for the relaxation limit on bounded time intervals, see [8] and the recent review [ 40 ].”
Long Time Behavior of Solutions to the 3D Compressible Euler Equations with Damping (2003, background): “The system under consideration is an example of a hyperbolic relaxation system, the general study of which has received considerable attention, see [4, 24, 35], for example.”
Asymptotic behavior of smooth solutions for partially dissipative hyperbolic systems with a convex entropy (2007, background): “strictly convex entropy function E = E(u), a first natural assumption is the entropy dissipation condition, see [5, 27, 31, 37], namely for every u, u ∈ Ω, with g(u) = 0, (E′(u) − E′(u)) · g(u) ≤ 0, where E′(u) is considered as a vector in R and · is the scalar product in the same space.”