Large time behaviour of Hele-Shaw flow with injection or suction for perturbations of balls in RN

E. Vondenhoff
2010 IMA Journal of Applied Mathematics  
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 decay properties are derived using energy estimates in Sobolev spaces.
doi:10.1093/imamat/hxp037 fatcat:o7e52xa5ofdotovgczogeuxowe