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On the Well-posedness of Some generalized Characteristic Cauchy Problems

Jean-André Marti 1 Victor Devoue 1 Antoine Delcroix 2 Allaud Emmanuel 1 Vernaeve Hans 3
1 CEREGMIA - Centre de Recherche en Economie, Gestion, Modélisation et Informatique Appliquée
2 CRREF - Centre de recherches et de ressources en éducation et formation
3 UGENT - Ghent University [Belgium]
Abstract : By means of convenient regularization for an ill posed Cauchy problem, we define an associated generalized problem and discuss the conditions for the solvability of it. To illustrate this, starting from the semilinear unidirectional wave equation with data given on a characteristic curve, we show existence and uniqueness of the solution
Keywords : transport equation regularization of data regularisation of problems nonlinear problems nonlinear generalized functions distributions characteristic problems
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https://hal.univ-antilles.fr/hal-01529519
Contributor : Antoine Delcroix Connect in order to contact the contributor
Submitted on : Tuesday, May 30, 2017 - 11:14:39 PM
Last modification on : Wednesday, December 12, 2018 - 5:10:03 PM

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Jean-André Marti, Victor Devoue, Antoine Delcroix, Allaud Emmanuel, Vernaeve Hans. On the Well-posedness of Some generalized Characteristic Cauchy Problems . Mathematical Modelling of Natural Phenomena, EDP Sciences, 2016, 11 (2), pp.89-99. ⟨10.1051/mmnp/201611207⟩. ⟨hal-01529519⟩

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