Abstract
A new hyperbolic affine geometric flow with dissipative term is proposed. The equations satisfied by support functions and the graph of the curve under this dissipative flow give rise to fully nonlinear hyperbolic equations, we obtain the existence for local solutions of this flow by reducing the flow to a first-order system. The equations for both perimeter and area of closed curves under the flow are also obtained. Based on this, we show that for a closed curve, the solution of this flow converges to a point in finite time. Furthermore, by a method of LeFloch–Smocyk for studying the hyperbolic mean curvature flow, global existence of the solution is established.
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.
