论文标题
薄域中的接触Hele-shaw问题的渐近分析
Asymptotic analysis of a contact Hele-Shaw problem in a thin domain
论文作者
论文摘要
我们分析了薄域中自由边界的零表面张力的接触率$ω^{\ varepsilon}（t）。 使用多尺度分析，我们研究了该问题的渐近行为为$ \ varepsilon \至0，$，即，当薄域$ω^{\ varepsilon}（t）$缩水到间隔$（0，l）中。 $（\ varepsilon = 0），$定义了渐近近似的其他术语，并证明了适当的渐近估计，可以证明这种方法是合理的。 我们还假设在初始时间$ t = 0 $的情况下，我们还建立了[0，t] $ in [0，t] $的$ t \ in Corner Points的保存几何形状。
We analyze the contact Hele-Shaw problem with zero surface tension of a free boundary in a thin domain $Ω^{\varepsilon}(t).$ Under suitable conditions on the given data, the one-valued local classical solvability of the problem for each fixed value of the parameter $\varepsilon$ is proved. Using the multiscale analysis, we study the asymptotic behavior of this problem as $\varepsilon \to 0,$ i.e., when the thin domain $Ω^{\varepsilon}(t)$ is shrunk into the interval $(0, l).$ Namely, we find exact representation of the free boundary for $t\in[0,T],$ derive the corresponding limit problem $(\varepsilon= 0),$ define other terms of the asymptotic approximation and prove appropriate asymptotic estimates that justify this approach. We also establish the preserving geometry of the free boundary near corner points for $t\in[0,T]$ under assumption that free and fixed boundaries form right angles at the initial time $t=0$.
