Abstract
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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have