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Paradigmatic well posedness in some generalized characteristic Cauchy problems

Author

Listed:
  • 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)

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.

Suggested Citation

  • Emmanuel Allaud & Antoine Delcroix & Victor Dévoué & Jean-André Marti & Hans Vernaeve, 2012. "Paradigmatic well posedness in some generalized characteristic Cauchy problems," Documents de Travail 2012-01, CEREGMIA, Université des Antilles et de la Guyane.
    • Handle: RePEc:crg:wpaper:dt2012-01
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    File URL: http://www2.univ-ag.fr/RePEc/DT/DT2012-01_Allaud_al.pdf
    File Function: First version, 2012
    Download Restriction: no
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    References listed on IDEAS

    as
    1. Emmanuel Allaud & Victor Dévoué, 2010. "Generalized solutions to a characteristic Cauchy problem," Documents de Travail 2010-04, CEREGMIA, Université des Antilles et de la Guyane.
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