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<article xsi:noNamespaceSchemaLocation="http://jats.nlm.nih.gov/publishing/1.1/xsd/JATS-journalpublishing1-mathml3.xsd" dtd-version="1.1" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"><front><journal-meta><journal-id journal-id-type="publisher-id">JCER</journal-id><journal-title-group><journal-title>Journal of Contemporary Educational Research</journal-title></journal-title-group><issn>2208-8466</issn><eissn>2208-8474</eissn><publisher><publisher-name>Bio-Byword Scientific Publishing Pty. Ltd.</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.26689/jcer.v7i10.5468</article-id><article-categories><subj-group subj-group-type="heading"><subject>Article</subject></subj-group></article-categories><title>Dynamics of a Reaction-Diffusion System with  Quiescence</title><url>https://artdesignp.com/journal/JCER/7/10/10.26689/jcer.v7i10.5468</url><author>XuHuichao</author><pub-date pub-type="publication-year"><year>2023</year></pub-date><volume>7</volume><issue>10</issue><history><date date-type="pub"><published-time>2023-11-07</published-time></date></history><abstract>In this paper, the dynamical behavior of a reaction-diffusion system with quiescence in a closed environment is investigated. The global existence of the solution is obtained by the upper and lower solution method, and the dissipative structure of the system is derived by constructing Lyapunov functions.</abstract><keywords/></article-meta></front><body/><back><ref-list><ref id="B1" content-type="article"><label>1</label><element-citation publication-type="journal"><p>Malik T, Smith HL, 2006, A Resource-Based Model of Microbial Quiescence. J. Math. Biol., 2006(53): 231–252.</p><pub-id pub-id-type="doi"/></element-citation></ref><ref id="B2" content-type="article"><label>2</label><element-citation publication-type="journal"><p>Jäger W, Krömker S, Tang B, 1994, Quiescence and Transient Growth Dynamics in Chemostat Models. Math. Biosci., 1994(119): 225–239.</p><pub-id pub-id-type="doi"/></element-citation></ref><ref id="B3" content-type="article"><label>3</label><element-citation publication-type="journal"><p>Hillen T, 2003, Transport Equations with Resting Phases. Europ. J. Appl. Math., 2003(14): 613–636.</p><pub-id pub-id-type="doi"/></element-citation></ref><ref id="B4" content-type="article"><label>4</label><element-citation publication-type="journal"><p>Hadeler KP, 2008, Quiescent Phases and Stability. Linear Alge. Appl., 2008(428): 1620–1627.</p><pub-id pub-id-type="doi"/></element-citation></ref><ref id="B5" content-type="article"><label>5</label><element-citation publication-type="journal"><p>Hadeler KP, Lewis MA, 2002, Spatial Dynamics of the Diffusive Logistic Equation with a Sedentary Compartment.Can. Appl. Math. Q., 2002(10): 473–499.</p><pub-id pub-id-type="doi"/></element-citation></ref><ref id="B6" content-type="article"><label>6</label><element-citation publication-type="journal"><p>Smoller J, 1994, Shock Waves and Reaction Diffusion Equations, in Grundlehren der Mathematischen Wissenschaften, 2nd edn, Springer-Verlag, New York, 258.</p><pub-id pub-id-type="doi"/></element-citation></ref><ref id="B7" content-type="article"><label>7</label><element-citation publication-type="journal"><p>Henry D, 1981, Geometric Theory of Semilinear Parabolic Equations, in Lecture Notes in Mathematics, Springer-Verlag, Berlin-New York, 840.</p><pub-id pub-id-type="doi"/></element-citation></ref><ref id="B8" content-type="article"><label>8</label><element-citation publication-type="journal"><p>Pao CV, 1992, Nonlinear Parabolic and Elliptic Equations, Plenum Press, New York.</p><pub-id pub-id-type="doi"/></element-citation></ref><ref id="B9" content-type="article"><label>9</label><element-citation publication-type="journal"><p>Ye QX, Li ZY, 1994, Introduction to Reaction Diffusion Equations (in Chinese). Science Press, China.</p><pub-id pub-id-type="doi"/></element-citation></ref></ref-list></back></article>
