Abstract
A constructive existence proof is given for a dumbbell-shaped solution near the two-sphere limit for a model of a steadily rigidly rotating liquid drop held together by surface tension. The solution shape is similar to the small solidified glassy dumbbells found in the lunar soil returned by the Apollo 11 Mission. The model problem reduces to a Neumann problem for a nonlinear ordinary differential equation ζ" = F( s, ζ, ζ ′) of nonstandard type for which the differential inequality techniques of Nagumo do not apply and for which the resulting linearization does not satisfy standard maximum principles. Our analysis borrows techniques from singular perturbation theory for differential equations and is based on a linearization of the problem about an approximate solution given by two spheres connected with a narrow neck formed by a Delaunay surface.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
