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Generalized solutions to a characteristic Cauchy problem


  • Emmanuel Allaud

    (AOC, Université des Antilles et de la Guyane)

  • Victor Dévoué

    (CEREGMIA, Université des Antilles et de la Guyane)


In this paper we give a meaning to the nonlinear characteristic Cauchy problem for the Wave Equation in base form by replacing it by a family of non-characteristic ones. This leads to a well formulated problem in an appropriate algebra of generalized functions. We prove existence of a solution and we precise how it depends on the choice made. We also check that in the classical case (non-characteristic) our new solution coincides with the classical one.

Suggested Citation

  • 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.
  • Handle: RePEc:crg:wpaper:dt2010-04

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    algebras of generalized functions; nonlinear partial differential equations; characteristic Cauchy problem; wave equation;

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