Work

Lower estimate of blow-up time and blow-up rate for non-local curvature flows for plane curves

Year: 2025

Type: article

Abstract: This study examines several non-local curvature flows for plane curves with general rotation number. The flows investigated here are the area-preserving flow, the length-preserving flow, and the gradient flow of isoperimetric deficit. In a previous study, sufficient conditions for finite-time blow-up have been presented, and an upper bound for the blow-up time have been proposed. Here, we give estimates for solutions including at least two important applications. First, a lower bound for the blow-up time for the blow-up solutions is derived. Second, our estimate improves the blow-up rate of the blow-up solutions.

Source: Japan Journal of Industrial and Applied Mathematics

DOI: 10.1007/s13160-025-00690-w

Author: Takeyuki Nagasawa

Institution: Saitama University

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090

Funders: Saitama University, Japan Society for the Promotion of Science