Linearized stability analysis of surface diffusion for hypersurfaces with boundary contact
作者： Daniel Depner
关键词: Mathematics 、 Balanced flow 、 Boundary (topology) 、 Partial differential equation 、 Surface diffusion 、 Parametrization 、 Right angle 、 Mathematical analysis 、 Domain (mathematical analysis) 、 Work (thermodynamics)
摘要: The linearized stability of stationary solutions for surface diffusion is studied. We consider hypersurfaces that lie inside a fixed domain, touch its boundary with right angle and fulfill no-flux condition. formulate the geometric evolution law as partial differential equation help parametrization from Vogel [Vog00], which takes care possible curved boundary. For analysis we identify in work Garcke, Ito Kohsaka [GIK05] problem an H
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sci-hub.se 参考文章(16)
Daniel Depner, Stability analysis of geometric evolution equations with triple linesand boundary contact Universität Regensburg. ,(2010)
Harald Garcke, Kazuo Ito, Yoshihito Kohsaka, Linearized Stability Analysis of Stationary Solutions for Surface Diffusion with Boundary Conditions SIAM Journal on Mathematical Analysis. ,vol. 36, pp. 1031- 1056 ,(2005) , 10.1137/S0036141003437939
Thomas I. Vogel, Sufficient conditions for capillary surfaces to be energy minima Pacific Journal of Mathematics. ,vol. 194, pp. 469- 489 ,(2000) , 10.2140/PJM.2000.194.469
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
Jean E. Taylor, John W. Cahn, Linking anisotropic sharp and diffuse surface motion laws via gradient flows Journal of Statistical Physics. ,vol. 77, pp. 183- 197 ,(1994) , 10.1007/BF02186838
Fabrizio Dav�, Morton E. Gurtin, On the motion of a phase interface by surface diffusion Zeitschrift für Angewandte Mathematik und Physik. ,vol. 41, pp. 782- 811 ,(1990) , 10.1007/BF00945835
W. W. Mullins, Theory of Thermal Grooving Journal of Applied Physics. ,vol. 28, pp. 333- 339 ,(1957) , 10.1063/1.1722742
John W. Barrett, Harald Garcke, Robert Nürnberg, On the Variational Approximation of Combined Second and Fourth Order Geometric Evolution Equations SIAM Journal on Scientific Computing. ,vol. 29, pp. 1006- 1041 ,(2007) , 10.1137/060653974
John Barrett, Harald Garcke, Robert Nürnberg, Parametric Approximation of Surface Clusters driven by Isotropic and Anisotropic Surface Energies Interfaces and Free Boundaries. ,vol. 12, pp. 187- 234 ,(2010) , 10.4171/IFB/232
Antonio Ros, Enaldo Vergasta, Stability for hypersurfaces of constant mean curvature with free boundary Geometriae Dedicata. ,vol. 56, pp. 19- 33 ,(1995) , 10.1007/BF01263611