¹ [aff id="a01" orgname="University of Science and Technology of China" orgdiv1="Department of Mathematics"] University of Science and Technology of China, Department of Mathematics, [city]Hefei[/city] 230026, [country]China[/country].
E-mail: [email]mbliu@mail.ustc.edu.cn[/email] [/aff]
² [aff id="a02" orgname="University of Science and Technology of China" orgdiv1="Department of Mathematics"] University of Science and Technology of China, Department of Mathematics, [city]Hefei[/city] 230026, [country]China[/country].
E-mail: [email]czx@mail.ustc.edu.cn[/email] [/aff]

[abstract language=en] In this paper, we apply the invariant region theory [1] and the compensated compactness method [2] to study the singular limits of stiff relaxation and dominant diffusion for the Cauchy problem of a system of quadratic flux and the Le Roux system, and obtain the convergence of the solutions to the equilibrium states of these systems. [/abstract]

Key words: [keygrp scheme=nd] [keyword type=m language=en]Relaxation limit[/keyword], [keyword type=m language=en]dominant diffusion[/keyword], [keyword type=m language=en]entropy-entropy flux[/keyword], [keyword type=m language=en]equilibrium states[/keyword]. [/keygrp]

[abstract language=es] En este artículo aplicamos la teoría de la región invariante [1] y el método de la compactificación compensada [2] para estudiar los límites singulares de la relajación rígida y difusión dominante para el problema de Cauchy de un sistema de flujo cuadrático y el sistema Roux obteniendo la convergencia de las soluciones para el estado de equilibrio de esos sistemas. [/abstract]

Palabras clave: [keygrp scheme=nd] [keyword type=m language=es]Límite de relajamiento[/keyword], [keyword type=m language=es]difusión dominante[/keyword], [keyword type=m language=es]flujo par entropía−entropía[/keyword], [keyword type=m language=es]estados de equilibrio[/keyword]. [/keygrp]

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[ocitat][no]6[/no] [omonog][oauthor role=nd][fname]T.[/fname] [surname]TARTAR[/surname][/oauthor], [title language=en]Compensated compactness and applications to partial differential equations[/title], [subtitle]Nonlinear Analysis and Mechanics, Heriot-Watt symposium IV, Vol. 128[/subtitle], [oauthor role=nd][fname]R. J.[/fname] [surname]Knops[/surname][/oauthor] ed., [edition]Pitman Res. Notes Math. Ser.[/edition], [pubname]Longman Sci. Tech.[/pubname], [city]Harlow[/city], ([date dateiso="19790000"]1979[/date]), 136-192[/omonog].[/ocitat]

[ocitat] [no]7[/no] [omonog][oauthor role=nd][fname]T.[/fname] [surname]TARTAR[/surname][/oauthor], [title language=en]The compensated compactness method applied to systems of conservation laws, Systems of Nonlinear Partial Differential Equations[/title] ([oauthor role=nd][fname]J. M.[/fname] [surname]Ball[/surname][/oauthor], ed.), [pubname]NATO ASI Series[/pubname], [city]Reidel[/city], [date dateiso="19830000"]1983[/date][/omonog].[/ocitat]