<?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>S0034-74262017000100103</article-id>
<article-id pub-id-type="doi">10.15446/recolma.v51n1.66843</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[A convergent iterative method for a logistic chemotactic system]]></article-title>
<article-title xml:lang="es"><![CDATA[Un método iterativo convergente para un sistema logístico quimiotáctico]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Ruiz Vera]]></surname>
<given-names><![CDATA[Jorge Mauricio]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad Nacional de Colombia Facultad de Ciencias Departamento de Matemáticas]]></institution>
<addr-line><![CDATA[Bogotá ]]></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>103</fpage>
<lpage>117</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_arttext&amp;pid=S0034-74262017000100103&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_abstract&amp;pid=S0034-74262017000100103&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_pdf&amp;pid=S0034-74262017000100103&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[ABSTRACT In this paper we study a nonlinear system of differential equations arising in chemotaxis. The system consists of a PDE that describes the evolution of a population and another which models the concentration of a chemical substance. In particular, we prove the existence and uniqueness of nonnegative solutions via an iterative method. First, we generate a Cauchy sequence of approximate solutions from a linear modification of the original system. Next, some uniform bounds on the solutions are used to find a subsequence that converges weakly to the solution of the original system.]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[RESUMEN En este artículo estudiamos un sistema no lineal de ecuaciones diferenciales que aparecen en quimiotaxis. El sistema consiste de una EDP que describe la evolución de una población y otra que modela la concentración de una sustancia química. En particular, probamos la existencia y unicidad de soluciones no negativas vía un método iterativo. Primero generamos una sucesión de Cauchy de soluciones aproximadas a partir de una modificación lineal del sistema original. Luego, algunas cotas uniformes de las soluciones son usadas para encontrar una subsucesión débilmente convergente a la solución del sistema original.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[reaction-diffusion equations]]></kwd>
<kwd lng="en"><![CDATA[weak solution]]></kwd>
<kwd lng="en"><![CDATA[convergence]]></kwd>
<kwd lng="es"><![CDATA[ecuaciones de reacción-difusión]]></kwd>
<kwd lng="es"><![CDATA[solución débil]]></kwd>
<kwd lng="es"><![CDATA[convergencia]]></kwd>
</kwd-group>
</article-meta>
</front><back>
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