Large-time behaviour of Hele-Shaw flow with injection or suction for perturbations of balls in RN (submitted), electronic version

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 evolution equation. Global existence results and de-cay properties are derived using energy estimates in Sobolev spaces. AMS subject classifications: 35R35, 35K55, 76D27 Key words: moving-boundary problem, non-local parabolic equatio