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hal-00345090, version 2

Generalized solutions to a non Lipschitz Goursat problem

Victor Devoue () 1

Differential Equations & Applications 1, 2 (2009) 153-178

Abstract: 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.

  • 1:  Analyse Optimisation Controle (AOC)
  • Université des Antilles et de la Guyane
  • Domain : Mathematics/Analysis of PDEs
  • Keywords : non-linear partial differential equation – wave equation – Goursat problem – regularization of problems – algebras of generalized functions.
  • Available versions :  v1 (2008-12-09) v2 (2008-12-10)
 
  • hal-00345090, version 2
  • http://hal.archives-ouvertes.fr/hal-00345090
  • oai:hal.archives-ouvertes.fr:hal-00345090
  • From: Victor Devoue <>
  • Submitted on: Wednesday, 10 December 2008 04:48:34
  • Updated on: Monday, 11 May 2009 18:18:44