Asymptotic properties of solutions of the Hele-Shaw equation (Q1594451)

For the title problem considered in a time-dependent domain \(\Omega_t\) with one source, the author estimates from above the isoperimetric defect of \(\Omega_t\) in terms of the area of initial domain \(\Omega_0\). This allows under some explicitly formulated condition to prove the convergence of \(\Omega_t\) to the unit disk as time \(t\) goes to infinity. The proof is based on some properties of subharmonic functions associated with solutions of Hele-Shaw equation.