Paradigmatic well posedness in some generalized characteristic Cauchy problems

Emmanuel Allaud, Antoine Delcroix, Victor Dévoué, Jean-André Marti and Hans Vernaeve
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Emmanuel Allaud: CEREGMIA, Université des Antilles et de la Guyane, France
Antoine Delcroix: CRREF, IUFM de Guadeloupe, France
Victor Dévoué: CEREGMIA, Université des Antilles et de la Guyane, France
Jean-André Marti: CEREGMIA, Université des Antilles et de la Guyane, France
Hans Vernaeve: Department of Mathematics, Ghent University, Belgium

No 2012-01, Documents de Travail from CEREGMIA, Université des Antilles et de la Guyane

Abstract: By means of convenient regularization for an ill posed Cauchy problem, we deï¬ ne 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.

Pages: 10 pages
Date: 2012-01
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