Global Existence of Smooth Solutions for Partially Dissipative Hyperbolic Systems with a Convex Entropy

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Asymptotic behavior of smooth solutions for partially dissipative hyperbolic systems with a convex entropy (2007, methodology): “Now, as proved in [13], if the system is entropy dissipative a nd non-degenerate, the set of equilibrium points is locally reduced to a single s mooth manifold.”
Hypocoercivity (2006, background): “In the study of convergence to equilibrium for hyperbolic systems of conservation laws, this condition is known as Kawashima’s nondegeneracy condition [34, 29, 45].”
Large Time Asymptotics for Partially Dissipative Hyperbolic Systems (2011, methodology): “The form (4)–(5) was first introduced in [2] and it is, after a change of variables, the general form for the linearized operator of symmetrizable, strictly dissipative systems, in the sense of [13].”
The strong relaxation limit of the multidimensional isothermal Euler equations (2006, background): “For fixed τ > 0, the existence of global smooth solutions to (1) follows from a result by Yong [10] (which is the analogue of [2] in the multidimensional framework).”