Stability analysis for stationary solutions of the Mullins-Sekerka flow with boundary contact
作者： Harald Garcke , Maximilian Rauchecker
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摘要: We first give a complete linearized stability analysis around stationary solutions of the Mullins-Sekerka flow with $90^\circ$ contact angle in two space dimensions. The include flat interfaces, as well arcs circles. investigate different behaviour dependence properties solution, such its curvature and length, boundary domain at points. show that changes terms these parameters, ranging from exponential to instability. also result on nonlinear for curved boundaries.
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Giovanni Dore, Maximal regularity in $L^p$ spaces for an abstract Cauchy problem Advances in Differential Equations. ,vol. 5, pp. 293- 322 ,(2000)
Hans Triebel, Theory of function spaces ,(1983)
Klaus-Jochen Engel, Rainer Nagel, One-Parameter Semigroups for Linear Evolution Equations ,(1999)
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
Jan Prüss, Gieri Simonett, Rico Zacher, On convergence of solutions to equilibria for quasilinear parabolic problems Journal of Differential Equations. ,vol. 246, pp. 3902- 3931 ,(2009) , 10.1016/J.JDE.2008.10.034
Paolo Acquistapace, Brunello Terreni, On quasilinear parabolic systems Mathematische Annalen. ,vol. 282, pp. 315- 335 ,(1988) , 10.1007/BF01456978
Joachim Escher, Gieri Simonett, A Center Manifold Analysis for the Mullins–Sekerka Model Journal of Differential Equations. ,vol. 143, pp. 267- 292 ,(1998) , 10.1006/JDEQ.1997.3373
Daniel DEPNER, Harald GARCKE, Linearized stability analysis of surface diffusion for hypersurfaces with triple lines Hokkaido Mathematical Journal. ,vol. 42, pp. 11- 52 ,(2013) , 10.14492/HOKMJ/1362406637
Ei-ichi Hanzawa, Classical solutions of the Stefan problem Tohoku Mathematical Journal. ,vol. 33, pp. 297- 335 ,(1981) , 10.2748/TMJ/1178229399