Prolongation of classical solutions and singularities of generalized solutions

DOI10.1016/S0294-1449(16)30279-7zbMath0722.35025OpenAlexW2589568718MaRDI QIDQ755999

Mikio Tsuji

Publication date: 1990

Published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=AIHPC_1990__7_6_505_0

zbMATH Keywords

Cauchy problemsglobal classical solutionsformation of singularitiesRankin-Hugoniot's condition

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Shocks and singularities for hyperbolic equations (35L67) Initial value problems for nonlinear first-order PDEs (35F25)

Related Items

Characteristic vector fields for first order partial differential equations ⋮ Unnamed Item ⋮ The regularity of generalized solutions of Hamilton--Jacobi equations

Cites Work

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• Piecewise smooth solutions of a single conservation law exist
• On singularities of mappings of Euclidean spaces. I. Mappings of the plane into the plane
• Formation of singularities of Hamilton-Jacobi equation. II
• The Hamilton-Jacobi equation. A global approach
• A regularity theorem for conservation laws
• DISCONTINUOUS SOLUTIONS OF HYPERBOLIC SYSTEMS OF QUASILINEAR EQUATIONS
• Some Properties of Viscosity Solutions of Hamilton-Jacobi Equations
• Globally classical solutions for nonlinear equations of first order
• Formation of Shocks for a Single Conservation Law