Decay estimates for hyperbolic balance laws

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The Optimal Decay Estimates on the Framework of Besov Spaces for Generally Dissipative Systems (2014, methodology): “Later, the second author and Yong [14] removed the technical requirement on the dissipative entropy assumed in [10, 31] and gave a perfect definition of the entropy for (1.1) (see Definition 2.1) to develop the global-in-time existence of classical solutions, see [15].”
Global Classical Solutions for Partially Dissipative Hyperbolic System of Balance Laws (2012, methodology): “The crucial point in [24] is to employ the time-weighted energy method which was first developed in [27] for compressible Navier-Stokes equations (see also [21]), and this enables us to show the decay estimate for d ≥ 2 without assuming the L1 property on the initial data.”
Decay property of regularity-loss type for the Euler-Maxwell system (2011, methodology): “However, the dissipation matrix L is not real symmetric and therefore we can not apply the general theory on the dissipative structure developed in [20, 22, 10, 6, 24, 11, 1, 12] to our system.”