Singularities of solutions to semilinear wave equations

zbMath0388.35045MaRDI QIDQ1250564

Jeffrey Rauch

Publication date: 1979

Published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série (Search for Journal in Brave)

Mathematics Subject Classification ID

First-order nonlinear hyperbolic equations (35L60)

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On the propagation of smoothness for semilinear systems of Maxwell-Klein- Gordon type ⋮ Propagation of singularities of solutions to semilinear Schrödinger equations ⋮ Regularity of solutions to the Navier-Stokes equations ⋮ Regularity, local and microlocal analysis in theories of generalized functions ⋮ Anomalous solutions to nonlinear hyperbolic equations ⋮ Spreading of singularities at the boundary in semilinear hyperbolic mixed problems. I: Microlocal \(H^{s,s'}\) regularity ⋮ Microlocal analysis in nonlinear thermoelasticity ⋮ Geometric Optics for Surface Waves in Nonlinear Elasticity ⋮ Propagation of singularities for generalized solutions to nonlinear wave equations ⋮ Régularité microlocale pour des problèmes de Dirichlet non linéaires non caractéristiques d'ordre deux à bord peu régulier ⋮ Microlocal Regularity Theorems for Nonsmooth Pseudodifferential Operators and Applications to Nonlinear Problems ⋮ Propagation of mild singularities in higher dimensional thermoelasticity ⋮ Conormal and Piecewise Smooth Solutions to Quasilinear Wave Equations ⋮ Singularities Produced in Conormal Wave Interactions ⋮ On the singularities of solutions to 4-D semilinear dispersive wave equations ⋮ Interactions involving gliding rays in boundary problems for semilinear wave equations ⋮ Progressing wave solutions to certain nonlinear mixed problems ⋮ Propagation of singularities of solutions to semilinear boundary value problems ⋮ Propagation de la régularité locale de solutions d'équations hyperboliques non linéaires. (Propagation of local smoothness for solutions of nonlinear hyperbolic equations) ⋮ Pseudo—differential operators with finitely smooth symbols and their applications to quasilinear equations ⋮ Propagation de l'analyticité des solutions de systèmes hyperboliques non-linéaires ⋮ The reflection and interaction of the singularities of solutions to semilinear wave equation in higher space dimension ⋮ A Remark on the Sobolev Regularity of Classical Solutions to Uniformly Parabolic Equations ⋮ Remarks on propagation of singularities in thermoelasticity ⋮ Global singularity structures of weak solutions to 4- semilinear dispersive wave equations ⋮ Calcul symbolique et propagation des singularités pour les équations aux dérivées partielles non linéaires

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