ON THE SURFACE DIFFUSION FLOW
作者： Gieri Simonett , Joachim Escher , Uwe F. Mayer
DOI:
关键词:
摘要: In this paper we present recent existence, uniqueness, and stability results for the motion of immersed hypersurfaces driven by surface diffusion. We provide numerical simulations curves surfaces that exhibit creation singularities. Moreover, our show flow causes a loss embeddedness some initially embedded configurations.
参考文章(21)
Herbert Amann, Linear and Quasilinear Parabolic Problems Birkhäuser Basel. ,(1995) , 10.1007/978-3-0348-9221-6
Y. Giga, K. Ito, On pinching of curves moved by surface diffusion Preprint Series of Department of Mathematics, Hokkaido University. ,vol. 379, pp. 1- 12 ,(1997)
Gerhard Huisken, Flow by mean curvature of convex surfaces into spheres Journal of Differential Geometry. ,vol. 20, pp. 237- 266 ,(1984) , 10.4310/JDG/1214438998
Matthew A. Grayson, The heat equation shrinks embedded plane curves to round points Journal of Differential Geometry. ,vol. 26, pp. 285- 314 ,(1987) , 10.4310/JDG/1214441371
Gieri Simonett, Center manifolds for quasilinear reaction-diffusion systems Differential and Integral Equations. ,vol. 8, pp. 753- 796 ,(1995)
H. Blaine Lawson, Lectures on minimal submanifolds ,(1980)
Herbert Amann, Nonhomogeneous Linear and Quasilinear Elliptic and Parabolic Boundary Value Problems Vieweg+Teubner Verlag, Wiesbaden. pp. 9- 126 ,(1993) , 10.1007/978-3-663-11336-2_1
Alessandra Lunardi, Analytic Semigroups and Optimal Regularity in Parabolic Problems ,(1995)
M. Gage, R. S. Hamilton, The heat equation shrinking convex plane curves Journal of Differential Geometry. ,vol. 23, pp. 69- 96 ,(1986) , 10.4310/JDG/1214439902
J. W. Cahn, C. M. Elliott, A. Novick-Cohen, The Cahn–Hilliard equation with a concentration dependent mobility: motion by minus the Laplacian of the mean curvature European Journal of Applied Mathematics. ,vol. 7, pp. 287- 301 ,(1996) , 10.1017/S0956792500002369