Interaction d'ondes simples pour des équations complètement non-linéaires

DOI10.24033/asens.1552zbMath0665.35051OpenAlexW2467735929MaRDI QIDQ3816438

Serge Alinhac

Publication date: 1988

Published in: Annales scientifiques de l'École normale supérieure (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=ASENS_1988_4_21_1_91_0

zbMATH Keywords

linearizationCauchy problemsdomain of influencesemilinearcharacteristic hypersurfacescompletely nonlinear\(C^{\infty }\) singularitiesconormal datainteraction of simple waves

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Shocks and singularities for hyperbolic equations (35L67) Analyticity in context of PDEs (35A20) Geometric theory, characteristics, transformations in context of PDEs (35A30) Higher-order nonlinear hyperbolic equations (35L75)

Related Items (10)

Régularité de la solution d'un problème de Cauchy fortement non linéaire à données singulières en un point. (Regularity of the solution of a strongly nonlinear Cauchy problem with singular data in a point) ⋮ Singularités des solutions d'équations d'ondes semi-linéaires ⋮ Tangent interation of co-normal waves for second order full nonlinear strickly hyperbolic equations ⋮ Singularites Conormales Non-Lipschitziennes Pour Des Lois De Conservation Scalaires Incompressibles ⋮ Nonlinear interaction of three impulsive gravitational waves. II: The wave estimates ⋮ On the Cauchy problem for gravity water waves ⋮ The motion of the particles of a two-dimensional ideal incompressible fluid ⋮ Conservation of Geometric Structures for Non-Homogeneous Inviscid Incompressible Fluids ⋮ Persistance de structures géométriques et limite non visqueuse pour les fluides incompressibles en dimension quelconque ⋮ Ondes semi-linéaires conormales par rapport à deux hypersurfaces transverses. (Conormal semilinear waves with respect to two transversal hypersurfaces)

Cites Work

• Interactions de singularités pour une classe d'équations à caractéristiques doubles
• Self-spreading and strength of singularities for solutions to semilinear wave equations
• Interaction of nonlinear progressing waves for semilinear wave equations
• Régularité microlocale pour des problèmes aux limites non linéaires. (Microlocal regularity for nonlinear boundary value problems)
• Propagation of singularities for semilinear hyperbolic equations in one space variable
• Jump discontinuities of semilinear, strictly hyperbolic systems in two variables: creation and propagation
• Nonlinear microlocal analysis of semilinear hyperbolic systems in one space dimension
• Propagation du front d'onde \(C^ p\) pour des équations non linéaires
• Propagation of C ∞ Regularity for Fully Nonlinear Second Order Strictly Hyperbolic Equations in Two Variables
• Subelliptic Non Linear Oblique Derivative Problems
• Propagation of analytic regularity for analytic fully nonlinear second order strictly hyperbolic equations in two variables
• Paracomposition et operateurs paradifferentiels
• Solutions conormales analytiques d'equations hyperboliques non lineaires
• Calcul symbolique et propagation des singularités pour les équations aux dérivées partielles non linéaires
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