Large-Time Behavior of Periodic Entropy Solutions to Anisotropic Degenerate Parabolic-Hyperbolic Equations

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dc.creatorChen, Gui-Qiang
dc.creatorPerthame, Benoit
dc.date2008-10-16
dc.date.accessioned2026-07-07T10:10:37Z
dc.date.available2026-07-07T10:10:37Z
dc.descriptionWe are interested in the large-time behavior of periodic entropy solutions in $L^\infty$ to anisotropic degenerate parabolic-hyperbolic equations of second-order. Unlike the pure hyperbolic case, the nonlinear equation is no longer self-similar invariant and the diffusion term in the equation significantly affects the large-time behavior of solutions; thus the approach developed earlier based on the self-similar scaling does not directly apply. In this paper, we develop another approach for establishing the decay of periodic solutions for anisotropic degenerate parabolic-hyperbolic equations. The proof is based on the kinetic formulation of entropy solutions. It involves time translations and a monotonicity-in-time property of entropy solutions, and employs the advantages of the precise kinetic equation for the solutions in order to recognize the role of nonlinearity-diffusivity of the equation.
dc.description10 pages
dc.identifierhttps://arxiv.org/abs/0810.2862
dc.identifierhttp://arxiv.org/abs/0810.2862
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/171648
dc.subjectAnalysis of PDEs
dc.subjectMathematical Physics
dc.subject35K65, 35K15, 35B10, 35B40, 35D99
dc.titleLarge-Time Behavior of Periodic Entropy Solutions to Anisotropic Degenerate Parabolic-Hyperbolic Equations
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