The Hele-Shaw problem with surface tension in a half-plane: A model problem
نویسندگان
چکیده
منابع مشابه
On Hele-shaw Models with Surface Tension
It is shown that surface tension effects on the free boundary have a regularizing effect for Hele-Shaw models, which implies existence and uniqueness of classical solutions for general initial domains.
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Morphological instabilities are common to pattern formation problems such as the non-equilibrium growth of crystals and directional solidification. Very small perturbations caused by noise originate convoluted interfacial patterns when surface tension is small. The generic mechanisms in the formation of these complex patterns are present in the simpler problem of a Hele-Shaw interface. Amid thi...
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It is shown that surface tension effects on the free boundary are regularizing for Hele-Shaw models. This implies, in particular, existence and uniqueness of classical solutions for a large class of initial data. As a consequence, we give a rigorous proof of the fact that homogeneous Hele-Shaw flows with positive surface tension are volume preserving and area shrinking.
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ژورنال
عنوان ژورنال: Journal of Differential Equations
سال: 2005
ISSN: 0022-0396
DOI: 10.1016/j.jde.2005.03.007