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Ondes de Gradients Multidimensionnelles
Monique Sablé-Tougeron

Memoirs of the American Mathematical Society
1993; 93 pp; softcover
Volume: 106
ISBN-10: 0-8218-2573-9
ISBN-13: 978-0-8218-2573-0
List Price: US$36
Individual Members: US$21.60
Institutional Members: US$28.80
Order Code: MEMO/106/511
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Recent techniques in partial differential equations have led to a solution to the general multidimensional Cauchy problem for nonlinear gradient waves. In a blown-up configuration, Sablé-Tougeron constructs a local solution for a quasilinear hyperbolic system with continuous Cauchy data, in which the first derivatives are discontinuous on a hypersurface. This strong singularity is not so problematic as a rarefaction: The use of Alinhac's para-unknown leads to a tame inequality without loss of derivatives for the iterative scheme.


Advanced graduate students studying partial differential equations. Researchers in nonlinear hyperbolic problems.

Table of Contents

  • Formulation du problème, énoncé du résultat
  • L'inégalité \(L^2\)
  • Espaces et calcul paradifférentiel adaptés
  • L'inégalité tame: première étape, paralinéarisation
  • L'inégalité tame, \(2^{\mathrm{ème}}\) étape: inégalités conormales du modèle paradifférentiel
  • L'inégalité tame fermée
  • Les estimations \(L^\infty\)
  • Les équations eiconales
  • Le problème non linéaire
  • Appendice
  • Bibliographie
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