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] mentioned in the flow curve \The ORDER of X (u, t) = (x (u, t), Y (u, t)): [a, b] × [0, ∞) → R 2 is a family of plane closed curve and X (u, 0) = X 0 (u) is a plane closed convex curves. Of curvature of the flow equations is: X t = (k-λ2π/L- (1-λ) L/2A) N, 0 ≤ λ ≤ 1, L = integral from n = a to b (| X u | du) = integral from n = a to b ((x u 2 y u 2 du) 1/2 ), A = 1/2 integral from n = a to b (xdy-ydx) = 1/2 integral from n = a to b (x (?) y / (?) uy (?) x / (?) u) du, X (u, 0) = X 0 (u), wherein X = X (u, t) represents the curve of the position vector at time t, L = L (t) is the length of the evolution curve representative of the A = A (t) area of ??the parameter u is not necessarily the arc length parameter, the unit normal vector is represented by N, k the evolution of the relative curvature of the curve, the subscript represents the guide number, λ is a normal number of t. We will prove this stream shorten the evolution of the perimeter of the convex curve, but increasing the area surrounded by the evolution of the curve, and evolution in the evolution of a curve become increasingly round, eventually, when the time tends to infinity, The shape of the curve converges to a circle. The article is mainly composed of three parts. The first part briefly introduced the curvature flow theory, history and background, as well as the model of this paper and the main conclusions; In the second part, we give some overall nature of the plane closed curve and general plane curve flow Geometrical evolution equation, since these The conclusions are known results, our only conclusion is given its provenance, spent proven details. The third part is the subject of this article. Here we give a new evolutionary model of plane convex curve, then, to prove the convexity convex curve remains in the process of evolution, and ultimately in the Hausdorff metric, when the time tends to infinity, converges to a circle. Then we will show that the evolution of the problem is equivalent to an initial value problem of nonlinear partial differential - integral equations using the maximum principle and the Leray-Schauder fixed point principle in the local sense the existence and uniqueness of the classical solution. Then prove global existence and uniqueness of the classical solution of the initial value problem by. Finally, to prove evolution curve C 2 and C ∞ converge to the circle.
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