Non-monotone perturbations for nonlinear parabolic equations associated with subdifferential operators = 劣微分作用素の付随した非線型放物型方程式に対する非単調作用素の摂動
Non-monotone perturbations for nonlinear parabolic equations associated with subdifferential operators = 劣微分作用素の付随した非線型放物型方程式に対する非単調作用素の摂動
复制标题
与次微分算子关联的非线性抛物线方程的非单调扰动 = 与次微分算子关联的非线性抛物线方程的非单调扰动
DOI：
10.1023/a:1004570921372
复制
发表时间：
1978
影响因子：
1.6
通讯作者：
大谷 光春
中科院分区：
文献类型：
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作者：
大谷 光春
近年来提出了基于能量不可微梯度系统的面形晶体生长模型和晶界模型。在本文中，我们研究了它们的最基本形式sut=(ux/|ux|)xandut=(1/a)(aux/|ux|)x，其中两个相关能量都包含一个在ux=0时不可导的1次方项|ux|。第一个方程是空间齐次的，而第二个方程在依赖于x时是空间非齐次的。这些方程通过其奇异扩散系数（无限大扩散常数）自然地表达非局部相互作用，这使得解的轮廓完全平坦。解释了证明和分析这些方程的数学基础，理论和数值方法显示了方程的解是如何演变的。
Recently models of faceted crystal growth and of grain boundaries were proposed based on the gradient system with nondifferentiable energy. In this article, we study their most basic forms given by the equationsut=(ux/|ux|)xandut=(1/a)(aux/|ux|)x, where both of the related energies include a |ux| term of power one which is nondifferentiable atux=0. The first equation is spatially homogeneous, while the second one is spatially inhomogeneous whenadepends onx. These equations naturally express nonlocal interactions through their singular diffusivities (infinitely large diffusion constant), which make the profiles of the solutions completely flat. The mathematical basis for justifying and analyzing these equations is explained, and theoretical and numerical approaches show how the solutions of the equations evolve.