LIFE SPAN OF A SMOOTH SOLUTION FOR THE SURFACE DIFFUSION FLOW
LIFE SPAN OF A SMOOTH SOLUTION FOR THE SURFACE DIFFUSION FLOW
摘要
Consider the motion of immersed hypersurfaces driven by surface diffusion flow and give anlower bound on the life span of a smooth immersed solution, which depends only on how muchthe curvature of the initial surface is concentrated in space.
基金
Project supported by the National Natural Science Foundation of China(No.10071067)and the Jiangsu Provincial Natural Science Foundation of China.
参考文献19
-
1Baras, P., Duchen, J. & Robert, R., Evolution d'une interface par diffusion de surface, Comm. Partial differential Equations, 9(1984), 313-335.
-
2Cahn, J. W., Elliott, C. M. & Novich-Cohn, A., The Cahn-Hilliard equation with a concentration dependent mobility: Motion by minus the Laplacian of the mean curvature, European J. Appl. Math.,7(1996), 287-301.
-
3Cahn, J. W. & Taylor, J. E., Surface motion by surface diffusion, Acta Metall. Mater., 42(1994),1045-1063.
-
4Chrusciel, P. T., Semi-global existence and convergence of solutions of the Robinson-Trautman (2-dimensional Calaibi equations), Comm. Math. Phys., 137(1991), 289-313.
-
5Davi, F. & Gurtin, M. E., On the motion of a phase interface by surface diffusion, Z. Angew. Math.Phys., 41(1990), 782-811.
-
6Elliot, C. M. & Garcke, H., Existence results for geometric interface models for surface diffusion, Adv.Math. Sci. Appl., 7(1997), 467-490.
-
7Escher, J., Mayer, U. F. & Simonett, G., The surface diffusion flow for immersed hypersurfaces, SIAM J. Math. Anal., 29(1998), 1419-1433.
-
8Giga, Y. & Ito, K., On pinching of curves moved by surface diffusion, Commun. Appl. Anal., 2(1998),393-405.
-
9Hamilton, R. S., Three-manifolds with positive Ricci curvature, J. Diff. Geom., 17(1982), 255-306.
-
10Huisken, G., Flow by mean curvature of convex surfaces into sphere, J. Diff. Geom., 20(1984), 237-266.
-
1吴加勇.SOME EXTENSIONS OF THE MEAN CURVATURE FLOW IN RIEMANNIAN MANIFOLDS[J].Acta Mathematica Scientia,2013,33(1):171-186. 被引量：1
-
2王琪.非负曲率空间形式中常高阶平均曲率的子流形[J].云南师范大学学报（自然科学版）,2013,33(1):29-33.
-
3Wei-guo ZhangDepartment of Basic Sciences, University of Shanghai for Science and Technology, Shanghai 200093, China.Cauchy Problem for Quasilinear Hyperbolic Systems with Higher Order Dissipative Terms[J].Acta Mathematicae Applicatae Sinica,2003,19(1):71-82.
-
4王琪.常高阶平均曲率子流形的一个余维数约化定理[J].贵州师范大学学报（自然科学版）,2014,32(3):44-46.
-
5张鑫浩.度量矩阵在微分几何中的运用[J].高师理科学刊,2015,35(11):26-29.
-
6王有安,王艳玲.Existence and Life Span of Periodic Solutions for the First Order Quasilinear Hyperbolic Equations[J].Chinese Quarterly Journal of Mathematics,1997,12(3):87-94.
-
7周忆.LIFE SPAN OF CLASSICAL SOLUTIONS TO u_(tt)-u_(xx)=|u|^(1+a)[J].Chinese Annals of Mathematics,Series B,1992,13(2):230-243. 被引量：6
-
8喻丽菊,薛艳昉.高余维平均曲率流在第一奇异时间处的平均曲率[J].信阳师范学院学报（自然科学版）,2012,25(1):31-33.
-
9崔国忠,宋锦萍.GLOBAL EXISTENCE OF SMOOTH SOLUTION FOR BOLTZMANN-POISSON SYSTEM WITH SMALL DATA[J].Acta Mathematica Scientia,2000,20(2):189-198.
-
10Hongbing QIU,Yunhua YE,Anqiang ZHU.The Extension of the H^k Mean Curvature Flow in Riemannian Manifolds[J].Chinese Annals of Mathematics,Series B,2014,35(2):191-208.
