Progressing wave solutions to certain nonlinear mixed problems

DOI10.1215/S0012-7094-86-05307-XzbMath0613.35050OpenAlexW1532490987MaRDI QIDQ1819292

Michael Beals, 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/s0012-7094-86-05307-x

zbMATH Keywords

smooth solutionspropagation of singularitiesconormalitymicrolocallynonlinear mixed problemscharacteristic completenessprogressing wave solutionssingle characteristic hypersurface

Mathematics Subject Classification ID

Shocks and singularities for hyperbolic equations (35L67) Second-order nonlinear hyperbolic equations (35L70) Analyticity in context of PDEs (35A20) Microlocal methods and methods of sheaf theory and homological algebra applied to PDEs (35A27) Geometric theory, characteristics, transformations in context of PDEs (35A30)

Related Items (9)

Reflection of transversal progressing waves for semilinear strictly hyperbolic systems ⋮ Problème mixte hyperbolique avec saut sur la condition aux limites. (A mixed hyperbolic problem with jump in the boundary condition) ⋮ Reflection and interaction of progressing waves for semilinear wave equations ⋮ Interaction of two nonlinear waves at the boundary ⋮ Interaction of shock and conormal singularities for conservation laws ⋮ Spreading of singularities at the boundary in semilinear hyperbolic mixed problems. I: Microlocal \(H^{s,s'}\) regularity ⋮ Transmission of progressing waves across a moving interface ⋮ Singularités des solutions d'équations d'ondes semi-linéaires ⋮ Classical conormal solution of semilinear systems

Cites Work

• Self-spreading and strength of singularities for solutions to semilinear wave equations
• Interaction of nonlinear progressing waves for semilinear wave equations
• Propagation of singularities for semilinear hyperbolic equations in one space variable
• Reflection of singularities of one-dimensional semilinear wave equations at boundaries
• Nonlinear microlocal analysis of semilinear hyperbolic systems in one space dimension
• Singularities of solutions to semilinear wave equations
• Mixed problems for hyperbolic equations. I: Energy inequalities
• Mixed problems for hyperbolic equations. II: Existence theorems with zero initial datas and energy inequalities with initial datas
• Calcul symbolique et propagation des singularités pour les équations aux dérivées partielles non linéaires
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