On a property of a classical solution of the nonlinear mass transport equation ut=uxx/1+ux2. II
On a property of a classical solution of the nonlinear mass transport equation ut=uxx/1+ux2. II
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关于非线性质量传递方程 ut=uxx/1 ux2 的经典解的性质。
DOI：
10.1063/1.527638
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发表时间：
1986
影响因子：
1.3
通讯作者：
H. Umehara
中科院分区：
文献类型：
--
作者：
A. Kitada;H. Umehara
Mullins [W. W. Mullins，J.Appl.Phys.28，333（1957）; 30，77（1959）]中关于u（x，t）表示曲面轮廓演化的非线性抛物方程的R1（真实的直线）中的柯西问题（P）：ut=uxx/1+ ux 2，（x，t）∈ R1×（0，∞）; u（x，0）=α（x），x∈ R1[模型（P）]。本文证明了Mullins模型（P）中初始表面α（x）的各峰高不随时间增加。
A mechanism of smoothing due to evaporation–condensation of the roughly perturbed surface of solid is described by Mullins [W. W. Mullins, J. Appl. Phys. 28, 333 (1957); 30, 77 (1959)] in terms of the Cauchy problem (P) in R1 (real line) of a nonlinear parabolic equation for u(x,t) representing the evolution of the profile of the surface: ut=uxx/1+ux2, (x,t)∈ R1×(0,∞); u(x,0)=α(x), x∈ R1[model (P)]. In the present paper, it is demonstrated that each peak height of the initial surface α(x) in Mullins’ model (P) does not increase with time.