Muskat问题的抛物域
The domain of parabolicity for the Muskat problem
摘要：
我们解决的Muskat问题的适定性在一个周期性的几何形状，并在一个设置，使我们能够考虑一般的初始和边界数据，重力效应，以及表面张力的影响。在没有表面张力的情况下，我们证明了瑞利-泰勒条件确定了一个域的抛物线的Muskat问题。这个属性用于建立问题的适定性。在表面张力效应的存在下，Muskat问题是抛物型的一般初始和边界数据。作为我们分析的一个双积，我们得到了与某些衍射问题相关的Dirichlet-Neumann型算子是小Hölder空间尺度上强连续和解析半群的负生成元.
英文摘要：
We address the well-posedness of the Muskat problem in a periodic geometry and in a setting which allows us to consider general initial and boundary data, gravity effects, as well as surface tension effects. In the absence of surface tension we prove that the Rayleigh-Taylor condition identifies a domain of parabolicity for the Muskat problem. This property is used to establish the well-posedness of the problem. In the presence of surface tension effects the Muskat problem is of parabolic type for general initial and boundary data. As a bi-product of our analysis we obtain that Dirichlet-Neumann type operators associated with certain diffraction problems are negative generators of strongly continuous and analytic semigroups in the scale of small Hölder spaces.
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