On local solutions of some mildly degenerate hyperbolic equations

DOI10.1016/0362-546X(93)90001-9zbMath0808.35076OpenAlexW2050119675MaRDI QIDQ4291638

Helvécio Rubens Crippa

Publication date: 5 March 1995

Published in: Nonlinear Analysis: Theory, Methods & Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0362-546x(93)90001-9

zbMATH Keywords

Cauchy problemnonlocal hyperbolic equationsabstract Kirchhoff-type equation

Mathematics Subject Classification ID

Second-order nonlinear hyperbolic equations (35L70)

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Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On a global solution of some quasilinear hyperbolic equation
• Infinite-dimensional dynamical systems in mechanics and physics
• Local solutions for a nonlinear degenerate Hyperbolic equation
• Some nonlinear degenerate wave equations
• On classical solutions of a quasilinear hyperbolic equation
• On local strong solutions of a nonlinear partial differential equation
• The initial value problem for a stretched string
• Mathematical analysis of the nonlinear model for the vibrations of a string
• The initial value problem for a nonlinear semi-infinite string
• On the non-linear vibration problem of the elastic string