<?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>0034-7426</journal-id>
<journal-title><![CDATA[Revista Colombiana de Matemáticas]]></journal-title>
<abbrev-journal-title><![CDATA[Rev.colomb.mat.]]></abbrev-journal-title>
<issn>0034-7426</issn>
<publisher>
<publisher-name><![CDATA[Universidad Nacional de Colombia y Sociedad Colombiana de Matemáticas]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S0034-74262017000100083</article-id>
<article-id pub-id-type="doi">10.15446/recolma.v51n1.66839</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[Solution of a time fractional inverse advection-dispersion problem by discrete mollification]]></article-title>
<article-title xml:lang="es"><![CDATA[Solución de un problema inverso de advección-dispersión con derivada temporal fraccionaria por medio de molificación discreta]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Mejía]]></surname>
<given-names><![CDATA[Carlos]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Piedrahita H]]></surname>
<given-names><![CDATA[Alejandro]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
<xref ref-type="aff" rid="Aaf"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad Nacional de Colombia Escuela de Matemáticas Facultad de Ciencias]]></institution>
<addr-line><![CDATA[Medellín ]]></addr-line>
<country>Colombia</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Universidad de Antioquia Instituto de Matemáticas Instituto de Matemáticas]]></institution>
<addr-line><![CDATA[Medellín ]]></addr-line>
<country>Colombia</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>06</month>
<year>2017</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>06</month>
<year>2017</year>
</pub-date>
<volume>51</volume>
<numero>1</numero>
<fpage>83</fpage>
<lpage>102</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_arttext&amp;pid=S0034-74262017000100083&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_abstract&amp;pid=S0034-74262017000100083&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_pdf&amp;pid=S0034-74262017000100083&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[ABSTRACT We consider an inverse problem for a time fractional advection-dispersion equation in a 1-D semi-infinite setting. The fractional derivative is interpreted in the sense of Caputo and advection and dispersion coefficients are constant. The inverse problem consists on the recovery of the boundary distribution of solute concentration and dispersion flux from measured (noisy) data known at an interior location. This inverse problem is ill-posed and thus the numerical solution must include some regularization technique. Our approach is a finite difference space marching scheme enhanced by adaptive discrete mollification. Error estimates and illustrative numerical examples are provided.]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[RESUMEN Consideramos un problema inverso para una ecuación de advección-dispersión con derivada temporal fraccionaria, en una configuración unidimensional. La derivada fraccionaria se interpreta en el sentido de Caputo y las coeficientes de advección y de dispersión son constantes. El problema inverso involucra la reconstrucción simultánea de la concentración de soluto y del flujo de dispersión en una de las fronteras del dominio físico, a partir de lecturas de datos perturbados en un punto interior del dominio. Mostramos que el problema inverso es mal condicionado y por tanto una solución numérica del problema requiere de alguna técnica de regularización. Proponemos un esquema de diferencias finitas de marcha en el espacio, que utiliza molificación discreta como técnica de regularización. Se incluyen estimativos de error y ejemplos numéricos ilustrativos.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[Ill-posed problems]]></kwd>
<kwd lng="en"><![CDATA[Caputo fractional derivative]]></kwd>
<kwd lng="en"><![CDATA[time fractional inverse advection-dispersion problem]]></kwd>
<kwd lng="en"><![CDATA[finite differences]]></kwd>
<kwd lng="en"><![CDATA[mollification]]></kwd>
<kwd lng="es"><![CDATA[Problemas mal condicionados]]></kwd>
<kwd lng="es"><![CDATA[derivada fraccionarias de Caputo]]></kwd>
<kwd lng="es"><![CDATA[problema inverso de advección-dispersión con derivada temporal fraccionaria]]></kwd>
<kwd lng="es"><![CDATA[diferencias finitas]]></kwd>
<kwd lng="es"><![CDATA[molificación]]></kwd>
</kwd-group>
</article-meta>
</front><back>
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