摘要
This paper deals with a 1 / κ-type nonlocal flow for an initial convex closed curve γ⊂ R which preserves the convexity and the integral∫X(·,t)κα+1ds,α∈(-∞,∞), of the evolving curve X(· , t). Forα∈[1,∞),it is proved that this flow exists for all time t∈ [0 , ∞) and X(· , t) converges to a round circle in C norm as t→ ∞. For α∈ (- ∞, 1) , a discussion on the possible asymptotic behavior of the flow is also given.