Entropy and Global Existence for Hyperbolic Balance Laws

By Wen-An Yong. 2004

248 citations recorded by the source corpus.

Subfields: Applied Mathematics, Control and Systems Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/6c3fd6701ea5fb9e974cf76e702b4b98548a1f48

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In Applied Mathematics

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Citations in the corpus

Asymptotic behavior of smooth solutions for partially dissipative hyperbolic systems with a convex entropy (2007, background): “About the existence of a solution, we recall the following result [13, 38].”
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.”
Large Time Asymptotics for Partially Dissipative Hyperbolic Systems (2011, methodology): “Under these conditions, in [36] the existence of global smooth solutions in a neighborhood of We was proved, when the linearized system around We satisfies (SK).”
Decay estimates for hyperbolic balance laws (2009, background): “The details were later carried out in [3] for onedimensional problems and in [15] for multi-dimensional ones.”
Global Classical Solutions for Partially Dissipative Hyperbolic System of Balance Laws (2012, background): “Recently, under a technical requirement on the entropy dissipation and the [SK] stability condition, Yong in [36] proved the global existence of classical solutions in a neighborhood of a constant equilibrium Ū ∈ RN satisfying G(Ū) = 0.”
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].”
The strong relaxation limit of the multidimensional isothermal Euler equations (2006, methodology): “(It is not clear whether the result of [10] is independent of the relaxation time for an arbitrary system.”
RELATIVE ENTROPY IN HYPERBOLIC RELAXATION (2005, methodology): “The stabilizing role of entropy dissipation has been extensively analyzed [12, 17, 6] and leads to global existence results (at least near equilibria) for relaxation systems.”