NONLINEAR STABILITY OF STATIONARY SOLUTIONS FOR SURFACE DIFFUSION WITH BOUNDARY CONDITIONS

Garcke H; Ito K; Kohsaka Y

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NONLINEAR STABILITY OF STATIONARY SOLUTIONS FOR SURFACE DIFFUSION WITH BOUNDARY CONDITIONS

机译：具有边界条件的表面扩散的平稳解的非线性稳定性

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摘要

The volume-preserving fourth order surface diffusion flow has constant mean curvature hypersurfaces as stationary solutions. We show nonlinear stability of certain stationary curves in the plane which meet an exterior boundary with a prescribed contact angle. Methods include semigroup theory, energy arguments, geometric analysis, and variational calculus.

机译：保持体积的四阶表面扩散流具有恒定的平均曲率超曲面作为固定解。我们显示了平面中某些固定曲线的非线性稳定性，这些固定曲线遇到具有规定接触角的外部边界。方法包括半群论，能量论证，几何分析和变分演算。

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《SIAM Journal on Mathematical Analysis》 |2008年第2期|共25页
作者
Garcke H; Ito K; Kohsaka Y;
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正文语种 eng
中图分类数学分析;
关键词
surface diffusion; nonlinear stability; energy method; variational calculus; GEOMETRIC EVOLUTION-EQUATIONS; MOTION; AREA; FLOW;

机译：表面扩散;非线性稳定性;能量法;变分法;几何演化方程;运动;面积;流动;

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专利

1. NONLINEAR STABILITY OF STATIONARY SOLUTIONS FORSURFACE DIFFUSION WITH BOUNDARY CONDITIONS [J] . HARALD GARCKE, KAZUO ITO, YOSHIHITO KOHSAKA SIAM Journal on Mathematical Analysis . 2009,第2期

机译：具有边界条件的表面扩散的平稳解的非线性稳定性
2. NONLINEAR STABILITY OF STATIONARY SOLUTIONS FOR SURFACE DIFFUSION WITH BOUNDARY CONDITIONS [J] . Garcke H, Ito K, Kohsaka Y SIAM Journal on Mathematical Analysis . 2008,第2期

机译：具有边界条件的表面扩散的平稳解的非线性稳定性
3. Linearized stability analysis of stationary solutions for surface diffusion with boundary conditions [J] . Garcke H, Ito K, Kohsaka Y SIAM Journal on Mathematical Analysis . 2005,第4期

机译：具有边界条件的表面扩散平稳解的线性化稳定性分析
4. Asymptotically Lyapunov-Stable Solutions with Boundary and Internal Layers in the Stationary Reaction-Diffusion-Advection Problems with a Small Transfer [C] . M. A. Davydova, N. N. Nefedov, S. A. Zakharova International Conference on Finite Difference Methods . 2019

机译：渐近Lyapunov-稳定的解决方案，边界和内层在固定反应 - 扩散 - 平面问题中具有小转移
5. Classes of reaction diffusion equations with nonlinear boundary conditions [D] . Goddard, Jerome, II 2011

机译：具有非线性边界条件的反应扩散方程的类别
6. Existence and stability of stationary solutions to spatially extended autocatalytic and hypercyclic systems under global regulation and with nonlinear growth rates [O] . Alexander S. Bratus, Vladimir P. Posvyanskii, Artem S. Novozhilov -1

机译：全球调节下空间扩展自催化和高循环系统及非线性增长的存在与稳定性
7. Nonlinear stability of stationary solutions for surface diffusion with boundary conditions [O] . Garcke Harald, Ito Kazuo, Kohsaka Yoshihito 2008

机译：具有边界条件的表面扩散平稳解的非线性稳定性
8. Global Stability of Stationary Solutions of Reaction-Diffusion System [R] . Gardner, R. A. 1979

机译：反应扩散系统平稳解的全局稳定性

NONLINEAR STABILITY OF STATIONARY SOLUTIONS FOR SURFACE DIFFUSION WITH BOUNDARY CONDITIONS

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