# A second order gradient flow of p-elastic planar networks

## TL;DR

This paper introduces a second order gradient flow model for p-elastic planar networks, demonstrating long-term existence and convergence to energy-critical configurations.

## Contribution

It develops a novel implicit variational scheme to construct weak solutions for the p-elastic energy flow in planar theta-networks.

## Key findings

- Proved long-time existence of the flow.
- Established convergence to critical points.
- Constructed weak solutions via variational methods.

## Abstract

We consider a second order gradient flow of the p-elastic energy for a planar theta-network of three curves with fixed lengths. We construct a weak solution of the flow by means of an implicit variational scheme. We show long-time existence of the evolution and convergence to a critical point of the energy.