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<identifier>oai:HAL:hal-00345090v2</identifier>
<datestamp>2017-12-21</datestamp>
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<setSpec>subject:math</setSpec>
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<publisher>HAL CCSD</publisher>
<title lang=en>Generalized solutions to a non Lipschitz Goursat problem</title>
<creator>Devoue, Victor</creator>
<contributor>Analyse Optimisation Controle (AOC) ; Université des Antilles et de la Guyane (UAG)</contributor>
<description>International audience</description>
<source>Differential Equations & Applications</source>
<identifier>hal-00345090</identifier>
<identifier>https://hal.archives-ouvertes.fr/hal-00345090</identifier>
<identifier>https://hal.archives-ouvertes.fr/hal-00345090v2/document</identifier>
<identifier>https://hal.archives-ouvertes.fr/hal-00345090/file/Devoue-Goursat-wellposed-12-08.pdf</identifier>
<source>https://hal.archives-ouvertes.fr/hal-00345090</source>
<source>Differential Equations & Applications, 2009, 1 (2), pp.153-178</source>
<language>en</language>
<subject lang=en>algebras of generalized functions</subject>
<subject lang=en>non-linear partial differential equation</subject>
<subject lang=en>wave equation</subject>
<subject lang=en>Goursat problem</subject>
<subject lang=en>regularization of problems</subject>
<subject lang=en>algebras of generalized functions.</subject>
<subject>MSC : 35D05; 35L70; 46F30</subject>
<subject>[MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP]</subject>
<type>info:eu-repo/semantics/article</type>
<type>Journal articles</type>
<description lang=en>In this paper we investigate solutions to the semi-linear wave equation in canonical form with non Lipschitz non-linearity and distributions or other generalized functions as data. To give a meaning to the Goursat problem with irregular data, we replace it by a biparametric family of problems. The first parameter turns the problem into a family of Lipschitz problems, the second one regularizes the data. Finally, the problem is solved in an appropriate algebra. We show that the solution is equal to the non-regularized one. In the examples, we take advantage of our results to give a new approach of the blow-up problem.</description>
<date>2009-05</date>
<rights>info:eu-repo/semantics/OpenAccess</rights>
</dc>
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