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Ondes de Gradients Multidimensionnelles
 
Front Cover for Ondes de Gradients Multidimensionnelles
Available Formats:
Electronic ISBN: 978-1-4704-0088-0
Product Code: MEMO/106/511.E
List Price: $36.00
MAA Member Price: $32.40
AMS Member Price: $21.60
Front Cover for Ondes de Gradients Multidimensionnelles
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  • Front Cover for Ondes de Gradients Multidimensionnelles
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Ondes de Gradients Multidimensionnelles
Available Formats:
Electronic ISBN:  978-1-4704-0088-0
Product Code:  MEMO/106/511.E
List Price: $36.00
MAA Member Price: $32.40
AMS Member Price: $21.60
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 1061993; 93 pp
    MSC: Primary 35;

    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.

    Readership

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

  • Table of Contents
     
     
    • Chapters
    • 1. Formulation du problème, énoncé du résultat
    • 2. L’inégalité $L^2$
    • 3. Espaces et calcul paradifférentiel adaptés
    • 4. L’inégalité tame: première étape, paralinéarisation
    • 5. L’inégalité tame, $2^{\text {\`eme}}$ étape: inégalités conormales du modèle paradifférentiel
    • 6. L’inégalité tame fermée
    • 7. Les estimations $L^\infty $
    • 8. Les équations eiconales
    • 9. Le problème non linéaire
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Volume: 1061993; 93 pp
MSC: Primary 35;

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.

Readership

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

  • Chapters
  • 1. Formulation du problème, énoncé du résultat
  • 2. L’inégalité $L^2$
  • 3. Espaces et calcul paradifférentiel adaptés
  • 4. L’inégalité tame: première étape, paralinéarisation
  • 5. L’inégalité tame, $2^{\text {\`eme}}$ étape: inégalités conormales du modèle paradifférentiel
  • 6. L’inégalité tame fermée
  • 7. Les estimations $L^\infty $
  • 8. Les équations eiconales
  • 9. Le problème non linéaire
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