The occurrence of singularities in solutions of homogeneous systems of two first order quasilinear hyperbolic equations with smooth initial data

DOI10.1016/0165-2125(79)90030-1zbMath0417.35050OpenAlexW2051238622MaRDI QIDQ755046

Alan Jeffrey, Andrea Donato

Publication date: 1979

Published in: Wave Motion (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0165-2125(79)90030-1

zbMATH Keywords

singularitiesquasilinear hyperbolic systemsadditively separable Riemann invariantsbreakdown of the solutioninitial curve in the hodograph planelinear homogeneous wave equation

Mathematics Subject Classification ID

Shocks and singularities for hyperbolic equations (35L67) First-order nonlinear hyperbolic equations (35L60) Hyperbolic conservation laws (35L65) Analyticity in context of PDEs (35A20)

Related Items

Riemann invariants-like solutions for a class of rate-type materials ⋮ An exact description of nonlinear wave interaction processes ruled by \(2\times 2\) hyperbolic systems ⋮ Exceptional hyperbolic systems of Hamiltonian form ⋮ Linearization of nonautonomous models describing fluid filled elastic tubes and nonlinear elastic rods with variable cross-section ⋮ Group analysis for a linear hyperbolic equation arising from a quasilinear reducible system ⋮ Global regularity and formation of singularities of solutions to first order quasilinear hyperbolic systems

Cites Work

• On the influence of initial conditions on the motion of water confined within a tank
• Existence and nonexistence in the large of solutions of quasilinear wave equations
• Hyperbolic systems of conservation laws II
• Development of Singularities of Solutions of Nonlinear Hyperbolic Partial Differential Equations
• Exact Solution for the Vibrations of a Nonlinear Continuous Model String
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item