<?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>S0120-419X2021000100003</article-id>
<article-id pub-id-type="doi">10.18273/revint.v39n1-2021003</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[Properties of the Support of Solutions of a Class of 2-Dimensional Nonlinear Evolution Equations]]></article-title>
<article-title xml:lang="es"><![CDATA[Propiedades del soporte de soluciones de una clase de ecuaciones de evolución no lineales en dos dimensiones]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Bustamante]]></surname>
<given-names><![CDATA[Eddye]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Jiménez Urrea]]></surname>
<given-names><![CDATA[José]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad Nacional de Colombia  ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Colombia</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Universidad Nacional de Colombia  ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Colombia</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>06</month>
<year>2021</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>06</month>
<year>2021</year>
</pub-date>
<volume>39</volume>
<numero>1</numero>
<fpage>41</fpage>
<lpage>50</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_arttext&amp;pid=S0120-419X2021000100003&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_abstract&amp;pid=S0120-419X2021000100003&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_pdf&amp;pid=S0120-419X2021000100003&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract In this work we consider equations of the form     where P(D) is a two-dimensional differential operator, and l &#8712;. We prove that if u is a sufficiently smooth solution of the equation, such that supp u(0),supp u(T) &#8834; [&#8722;B, B] × [&#8722;B, B] for some B &gt; 0, then there exists R0 &gt; 0 such that supp u(t) &#8834; [&#8722;R0, R0]×[&#8722;R0, R0] for every t &#8712; [0, T].]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen En este trabajo consideramos ecuaciones de la forma     donde P(D) es un operador diferencial en dos dimensiones, y l &#8712;. Probamos que si u es una solución suficientemente suave de la ecuación, tal que supp u(0),supp u(T) &#8834; [&#8722;B, B] × [&#8722;B, B] para algún B &gt; 0, entonces existe R0 &gt; 0 tal que supp u(t) &#8834; [&#8722;R0, R0] × [&#8722;R0, R 0] para todo t &#8712; [0, T].]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[Nonlinear evolution equations]]></kwd>
<kwd lng="en"><![CDATA[weighted Sobolev spaces]]></kwd>
<kwd lng="en"><![CDATA[Carleman estimates]]></kwd>
<kwd lng="en"><![CDATA[MSC2010: 35Q53]]></kwd>
<kwd lng="en"><![CDATA[37L50]]></kwd>
<kwd lng="en"><![CDATA[47J35]]></kwd>
<kwd lng="es"><![CDATA[Ecuaciones de evolución no lineales]]></kwd>
<kwd lng="es"><![CDATA[espacios de Sobolev con peso]]></kwd>
<kwd lng="es"><![CDATA[estimativos Carleman]]></kwd>
</kwd-group>
</article-meta>
</front><back>
<ref-list>
<ref id="B1">
<label>[1]</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Ablowitz]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
</person-group>
<source><![CDATA[Nonlinear dispersive waves: asymptotic analysis and solitons]]></source>
<year>2011</year>
<publisher-name><![CDATA[Cambridge University Press]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B2">
<label>[2]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Benzekry]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Classical Mathematical Models for Description and Prediction of Experimental Tumor Growth]]></article-title>
<source><![CDATA[PLOS Comput. Biol]]></source>
<year>2014</year>
<volume>10</volume>
<numero>8</numero>
<issue>8</issue>
<page-range>1-19</page-range></nlm-citation>
</ref>
<ref id="B3">
<label>[3]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Biagioni]]></surname>
<given-names><![CDATA[H.A.]]></given-names>
</name>
<name>
<surname><![CDATA[Linares]]></surname>
<given-names><![CDATA[F.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Well-posedness results for the modified Zakharov-Kuznetsov equation]]></article-title>
<source><![CDATA[Birkhäuser, Basel]]></source>
<year>2003</year>
<volume>54</volume>
<page-range>181-9</page-range></nlm-citation>
</ref>
<ref id="B4">
<label>[4]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Bourgain]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[On the compactness of the support of solutions of dispersive equations]]></article-title>
<source><![CDATA[Internat. Math. Res. Notices]]></source>
<year>1997</year>
<numero>9</numero>
<issue>9</issue>
<page-range>437-47</page-range></nlm-citation>
</ref>
<ref id="B5">
<label>[5]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Bustamante]]></surname>
<given-names><![CDATA[E.]]></given-names>
</name>
<name>
<surname><![CDATA[Isaza]]></surname>
<given-names><![CDATA[P.]]></given-names>
</name>
<name>
<surname><![CDATA[Mejía]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[On uniqueness properties of solutions of the Zakharov&#8211;Kuznetsov equation]]></article-title>
<source><![CDATA[J. Funct. Anal]]></source>
<year>2013</year>
<volume>254</volume>
<numero>11</numero>
<issue>11</issue>
<page-range>2529-49</page-range></nlm-citation>
</ref>
<ref id="B6">
<label>[6]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Bustamante]]></surname>
<given-names><![CDATA[E.]]></given-names>
</name>
<name>
<surname><![CDATA[Isaza]]></surname>
<given-names><![CDATA[P.]]></given-names>
</name>
<name>
<surname><![CDATA[Mejía]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[On the support of solutions to de ZakharovKuznetsov equation]]></article-title>
<source><![CDATA[J. Differential Equations]]></source>
<year>2011</year>
<volume>251</volume>
<numero>10</numero>
<issue>10</issue>
<page-range>2728-36</page-range></nlm-citation>
</ref>
<ref id="B7">
<label>[7]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Faminskii]]></surname>
<given-names><![CDATA[A.V.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[The Cauchy problem for the Zakharov-Kuznetsov equation]]></article-title>
<source><![CDATA[Differential Equations]]></source>
<year>1995</year>
<volume>31</volume>
<numero>6</numero>
<issue>6</issue>
<page-range>1002-12</page-range></nlm-citation>
</ref>
<ref id="B8">
<label>[8]</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Hall]]></surname>
<given-names><![CDATA[E.J.]]></given-names>
</name>
<name>
<surname><![CDATA[Giaccia]]></surname>
<given-names><![CDATA[A.J.]]></given-names>
</name>
</person-group>
<source><![CDATA[Radiobiology for the Radiologists]]></source>
<year>2018</year>
<edition>8th ed</edition>
<publisher-loc><![CDATA[Philadelphia ]]></publisher-loc>
<publisher-name><![CDATA[Lippincott Williams &amp; Wilkins (LWW)]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B9">
<label>[9]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Kenig]]></surname>
<given-names><![CDATA[C.]]></given-names>
</name>
<name>
<surname><![CDATA[Ponce]]></surname>
<given-names><![CDATA[G.]]></given-names>
</name>
<name>
<surname><![CDATA[Vega]]></surname>
<given-names><![CDATA[L.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[On the support of solutions to the generalized KdV equation]]></article-title>
<source><![CDATA[Ann. Inst. H. Poincaré Anal. Non Linéaire]]></source>
<year>2002</year>
<volume>19</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>2-191</page-range></nlm-citation>
</ref>
<ref id="B10">
<label>[10]</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Larkin]]></surname>
<given-names><![CDATA[N.A.]]></given-names>
</name>
</person-group>
<source><![CDATA[Kawahara-Burgers equation on a strip]]></source>
<year>2015</year>
<publisher-loc><![CDATA[Maringá ]]></publisher-loc>
<publisher-name><![CDATA[Adv. Math. Phys.]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B11">
<label>[11]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Larkin]]></surname>
<given-names><![CDATA[N.A.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[The 2D Kawahara equation on a half-strip]]></article-title>
<source><![CDATA[Appl. Math. Optim]]></source>
<year>2014</year>
<volume>70</volume>
<numero>3</numero>
<issue>3</issue>
<page-range>443-68</page-range></nlm-citation>
</ref>
<ref id="B12">
<label>[12]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Linares]]></surname>
<given-names><![CDATA[F.]]></given-names>
</name>
<name>
<surname><![CDATA[Pastor]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Local and global well-posedness for the 2D generalizes Zakharov-Kuztnesov equation]]></article-title>
<source><![CDATA[J. Funct. Anal]]></source>
<year>2011</year>
<volume>260</volume>
<numero>4</numero>
<issue>4</issue>
<page-range>1060-85</page-range></nlm-citation>
</ref>
<ref id="B13">
<label>[13]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Linares]]></surname>
<given-names><![CDATA[F.]]></given-names>
</name>
<name>
<surname><![CDATA[Pastor]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Well-posedness for the two-dimensional modified ZakharovKuznetsov equation]]></article-title>
<source><![CDATA[SIAM J. Math. Anal]]></source>
<year>2009</year>
<volume>41</volume>
<numero>4</numero>
<issue>4</issue>
<page-range>1323-39</page-range></nlm-citation>
</ref>
<ref id="B14">
<label>[14]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Linares]]></surname>
<given-names><![CDATA[F.]]></given-names>
</name>
<name>
<surname><![CDATA[Pastor]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
<name>
<surname><![CDATA[Saut]]></surname>
<given-names><![CDATA[J.C.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Well-Posedness for the ZK Equation in a Cylinder and on the Background of a KdV Soliton]]></article-title>
<source><![CDATA[Comm. Partial Differential Equations]]></source>
<year>2010</year>
<volume>35</volume>
<numero>9</numero>
<issue>9</issue>
<page-range>1674-89</page-range></nlm-citation>
</ref>
<ref id="B15">
<label>[15]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Nahas]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Ponce]]></surname>
<given-names><![CDATA[G.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[On the persistent properties of solutions to semi-linear Schrödinger equation]]></article-title>
<source><![CDATA[Comm. Partial Differential Equations]]></source>
<year>2009</year>
<volume>34</volume>
<numero>10-12</numero>
<issue>10-12</issue>
<page-range>1208-27</page-range></nlm-citation>
</ref>
<ref id="B16">
<label>[16]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Panthee]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[A note on the unique continuation property for Zakharov-Kuznetsov equation]]></article-title>
<source><![CDATA[Nonlinear Anal]]></source>
<year>2004</year>
<volume>59</volume>
<numero>3</numero>
<issue>3</issue>
<page-range>425-38</page-range></nlm-citation>
</ref>
<ref id="B17">
<label>[17]</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Tao]]></surname>
<given-names><![CDATA[T.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Published for the Conference Board of the Mathematical Sciences, Washington, DC]]></article-title>
<source><![CDATA[Nonlinear dispersive equations]]></source>
<year>2006</year>
<volume>106</volume>
<publisher-loc><![CDATA[Providence ]]></publisher-loc>
<publisher-name><![CDATA[by the American Mathematical Society]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B18">
<label>[18]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Zakharov]]></surname>
<given-names><![CDATA[V.E.]]></given-names>
</name>
<name>
<surname><![CDATA[Kuznetsov]]></surname>
<given-names><![CDATA[E.A.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[On three-dimensional solitons]]></article-title>
<source><![CDATA[Soviet Phys. JETP]]></source>
<year>1974</year>
<volume>29</volume>
<page-range>594-7</page-range></nlm-citation>
</ref>
</ref-list>
</back>
</article>
