Singularities of Singular Solutions of First-Order Differential Equations of Clairaut Type

A first-order differential equation of Clairaut type has a family of classical solutions, and a singular solution when the contact singular set is not empty. The projection of a singular solution of Clairaut type is an envelope of a family of fronts (Legendre immersions). In these cases, the envelop...

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Bibliographic Details
Published in:Journal of dynamical and control systems 2022-01, Vol.28 (1), p.19-41
Main Authors: Saji, Kentaro, Takahashi, Masatomo
Format: Article
Language:English
Subjects:
Calculus of Variations and Optimal Control
Optimization
Control
Dynamical Systems
Dynamical Systems and Ergodic Theory
Envelopes
Mathematical analysis
Mathematics
Mathematics and Statistics
Ordinary differential equations
Partial differential equations
Systems Theory
Vibration
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Summary:A first-order differential equation of Clairaut type has a family of classical solutions, and a singular solution when the contact singular set is not empty. The projection of a singular solution of Clairaut type is an envelope of a family of fronts (Legendre immersions). In these cases, the envelopes are always fronts. We investigate singular points of envelopes for first-order ordinary differential equations, first-order partial differential equations, and systems of first-order partial differential equations of Clairaut type, respectively.
ISSN:1079-2724
1573-8698
DOI:10.1007/s10883-020-09511-4