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<identifier>oai:HAL:hal-01679144v1</identifier>
<datestamp>2018-01-10</datestamp>
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<setSpec>subject:math</setSpec>
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<title lang=en>A null controllability problem with a finite number of constraints on the normal derivative for the semilinear heat equation</title>
<creator>Louis-Rose, Carole</creator>
<contributor>Centre de Recherche en Economie, Gestion, Modélisation et Informatique Appliquée (CEREGMIA) ; Université des Antilles et de la Guyane (UAG)</contributor>
<description>International audience</description>
<source>ISSN: 1417-3875</source>
<source>Electronic Journal of Qualitative Theory of Differential Equations</source>
<publisher>University of Szeged, Bolyai Institute</publisher>
<identifier>hal-01679144</identifier>
<identifier>https://hal.archives-ouvertes.fr/hal-01679144</identifier>
<source>https://hal.archives-ouvertes.fr/hal-01679144</source>
<source>Electronic Journal of Qualitative Theory of Differential Equations, University of Szeged, Bolyai Institute, 2012, pp.1 - 34. 〈10.14232/ejqtde.2012.1.95〉</source>
<identifier>DOI : 10.14232/ejqtde.2012.1.95</identifier>
<relation>info:eu-repo/semantics/altIdentifier/doi/10.14232/ejqtde.2012.1.95</relation>
<language>en</language>
<subject>[MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP]</subject>
<subject>[MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC]</subject>
<type>info:eu-repo/semantics/article</type>
<type>Journal articles</type>
<description lang=en>We consider the semilinear heat equation in a boundeddomain of R^m. We prove the null controllability of the systemwith a finite number of constraints on the normal derivative, whenthe control acts on a bounded subset of the domain. First, weshow that the problem can be transformed into a null controllabilityproblem with constraint on the control, for a linear system.Then, we use an appropriate observability inequality to solve thelinearized problem. Finally, we prove the main result by means ofa fixed-point method.</description>
<date>2012</date>
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