Two Kinds Of Combined Convex Curve Flows In Plane

In this paper,on the basis of the previous study,two kinds of combined convex curve flows are studied,one converge to the circle under the C0 norm,the other converge to the circle under the C?norm.First,the first kind of combined convex curve flow has been discussed:(?)=(?p(u,t)+(1-?)?(t)-1/k)N(u,t),0???1 It is shown that when the initial curve is a smooth closed curve,the curve flow remains convex during the development process.With the increase of time,the perimeter of the curve does not increase,the area of the closed pattern enclosed by the curve is not reduced,and it is proved that under the C0 norm,when timet??,the curve converges to a circle.Then the second kind of combined convex curve flow has been discussed:(?)=(L/2?-??(t)-(1-?)1/k)N(t),0???1 It is shown that when the initial curve is a smooth closed curve,the curve flow remains strictly convex during the development process,with the increase of time,the perimeter of the curve and the area of the closed pattern enclosed by the curve is increased monotonically,and it is proved that under the C0 norm,when time t?+?,the curve converges to a circle,and finally,under the C? norm,when time t?+?,the curve also converges to a finite circle.