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Large-time behaviour of Hele-Shaw flow with surface tension and with injection or suction in one point is discussed. We consider domains which are initially small perturbations of balls. Radially symmetric solutions are stationary after a suitable time-dependent rescaling. The evolution of perturbations can be described by a non-local nonlinear parabolic(More)
Long-time behaviour for the classical Hele-Shaw flow with injection in the origin is discussed. Domains that are small perturbations of balls are considered. Radially symmetric solutions are turned into stationary ones by suitable time-dependent scaling. An evolution equation for the motion of the domain is derived and linearised. Spectral properties of the(More)
We discuss long-time behaviour of the Hele-Shaw flow in R 3 with surface tension and injection or suction in the origin, for domains that are small perturbations of balls. After rescaling, radially symmetric solutions become stationary. We study the stability of these solutions. In particular, we show that all liquid can be removed by suction if the suction(More)
We show the existence of noncircular, self-similar solutions to the three-dimensional Hele-Shaw suction problem with surface tension regularisation up to complete extinction. In an appropriate scaling, these solutions are found as bifurcation solutions to a nonlocal elliptic equation of order three. The bifurcation parameter is the ratio of the suction(More)
A sufficient condition is presented for two-dimensional images on a finite rectangular domain Ω=(−A,A)×(−B,B) to be completely determined by features on curves t↦(ξ(t),t) in the three-dimensional domain Ω×(0,∞) of an α-scale space. For any fixed finite set of points in the image, the values of the α-scale space at these points at all scales together do not(More)
Radio Frequency (RF) switches of Micro Electro Mechanical Systems (MEMS) are appealing to the mobile industry because of their energy efficiency and ability to accommodate more frequency bands. However, the elec-tromechanical coupling of the electrical circuit to the mechanical components in RF MEMS switches is not fully understood. In this paper, we(More)
We present a stability result for a class of non-trivial self-similarly vanishing solutions to a 3D Hele-Shaw moving boundary problem with surface tension and single-point suction. These solutions are domains that bifurcate from the trivial spherical solution. The moving domains have a geometric centre located at the suction point and they are axially(More)
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