The Cauchy problem for semilinear hyperbolic systems with discontinuous data

DOI10.1215/S0012-7094-86-05349-4zbMath0631.35056OpenAlexW1503227847MaRDI QIDQ1094588

Guy Metivier

Publication date: 1986

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1215/s0012-7094-86-05349-4

zbMATH Keywords

existenceCauchy problemdiscontinuous datasuccessive approximationsemilinearstrictly hyperbolicconormal distributions

Mathematics Subject Classification ID

Shocks and singularities for hyperbolic equations (35L67) First-order nonlinear hyperbolic equations (35L60) PDEs with low regular coefficients and/or low regular data (35R05)

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Viscous approach of discontinuous solutions of semilinear symmetric hyperbolic systems, The semilinear second-order hyperbolic equation with data strongly singular at one point, Reflection of transversal progressing waves for semilinear strictly hyperbolic systems, Couches Limites: Un Problème Inverse, Analysis of strong singularities for nonlinear hyperbolic equations, The Cauchy problem for nonlinear hyperbolic equations with discontinuous data, Interaction of piecewise smooth progressing waves for semilinear hyperbolic equations, Multidimensional riemann problem for smilinear wave equations, The Cauchy problem for semilinear hyperbolic equations with cross discontinuous data, Classical conormal solution of semilinear systems, Existence d'ondes de rarefaction pour des systems quasi‐lineaires hyperboliques multidimensionnels, Justification of Multidimensional Single Phase Semilinear Geometric Optics, Ondes semi-linéaires conormales par rapport à deux hypersurfaces transverses. (Conormal semilinear waves with respect to two transversal hypersurfaces), NONLINEAR ASYMPTOTICS FOR HYPERBOLIC INTERNAL WAVES OF SMALL WIDTH, On the existence and cusp singularity of solutions to semilinear generalized Tricomi equations with discontinuous initial data, Nonlinear geometric optics for short pulses

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