<?xml version="1.0" encoding="ISO-8859-1"?><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<front>
<journal-meta>
<journal-id>0120-419X</journal-id>
<journal-title><![CDATA[Revista Integración]]></journal-title>
<abbrev-journal-title><![CDATA[Integración - UIS]]></abbrev-journal-title>
<issn>0120-419X</issn>
<publisher>
<publisher-name><![CDATA[Universidad Industrial de Santander]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S0120-419X2019000200261</article-id>
<article-id pub-id-type="doi">10.18273/revint.v37n2-2019004</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[The asymptotic analysis of a Darcy-Stokes system coupled through a curved interface]]></article-title>
<article-title xml:lang="es"><![CDATA[Análisis asintótico de un sistema Darcy-Stokes acoplado a través de una interfaz curva]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Morales]]></surname>
<given-names><![CDATA[Fernando A.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad Nacional de Colombia Escuela de Matemáticas ]]></institution>
<addr-line><![CDATA[Medellín ]]></addr-line>
<country>Colombia</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>12</month>
<year>2019</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>12</month>
<year>2019</year>
</pub-date>
<volume>37</volume>
<numero>2</numero>
<fpage>261</fpage>
<lpage>297</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_arttext&amp;pid=S0120-419X2019000200261&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_abstract&amp;pid=S0120-419X2019000200261&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_pdf&amp;pid=S0120-419X2019000200261&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract We present the asymptotic analysis of a Darcy-Stokes coupled system, modeling the fluid exchange between a narrow channel (Stokes flow) and a porous medium (Darcy flow), coupled through a C2 curved interface. The channel is a cylindrical domain between the interface (&#915;) and a parallel translation of itself   The introduction of a change variable (to fix the domain geometry) and the introduction of two systems of coordinates: the Cartesian and a local one (consistent with the geometry of the surface), permit to find the limiting form of the system when the width of the channel tends to zero (&#1108; &#8594; 0). The limit problem is a coupled system with Darcy flow in the porous medium and Brinkman flow on the curved interface (&#915;). MSC2010: 35K50, 35B25, 80A20, 35F15.]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen En el trabajo se presenta el análisis asintótico de un sistema Darcy-Stokes acoplado a través de una interfaz curva. El sistema modela el intercambio de fluido entre un canal angosto (flujo Stokes) y un medio poroso (flujo Darcy). El canal es un dominio cilíndrico definido entre la interfaz (&#915;) y una traslación paralela de dicha superficie   Utilizando un cambio de variables para fijar un dominio de referencia e introduciendo dos sistemas de coordenadas, el Cartesiano canónico y el local (consistente con la geometría de la superficie), es posible encontrar la forma límite cuando el ancho del canal tiende a cero (&#1108; - 0). El problema límite es un sistema acoplado con flujo Darcy en el medio poroso y flujo Brinkman en la interfaz (&#915;).]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[porous media]]></kwd>
<kwd lng="en"><![CDATA[curved interfaces]]></kwd>
<kwd lng="en"><![CDATA[Darcy-Stokes system]]></kwd>
<kwd lng="en"><![CDATA[Darcy-Brinkman system]]></kwd>
<kwd lng="es"><![CDATA[medio poroso]]></kwd>
<kwd lng="es"><![CDATA[interfaces curvas]]></kwd>
<kwd lng="es"><![CDATA[sistema Darcy-Stokes]]></kwd>
<kwd lng="es"><![CDATA[sistema Darcy-Brinkman]]></kwd>
</kwd-group>
</article-meta>
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