Stability of self-similar extinction solutions for a 3D Hele-Shaw suction problem
نویسندگان
چکیده
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 symmetric. We show stability with respect to perturbations that preserve these properties. AMS subject classification: 35R35, 76D27, 47J15
منابع مشابه
Non-trivial self-similar extinction solutions for a 3D Hele-Shaw suction problem
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 speed and the surface tension coefficient....
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