Large-time rescaling behaviors of some rational type solutions to the Polubarinova-Galin equation with injection
نویسنده
چکیده
The main goal of this paper is to give a precise description of rescaling behaviors of rational type global strong solutions to the PolubarinovaGalin equation. The Polubarinova-Galin equation is the reformulation of the zero surface tension Hele-Shaw problem with a single source at the origin by considering the moving domain as the Riemann mapping of the unit disk centered at the origin. The coefficients {ak(t)}k≥2 of the polynomial strong solution fk0(ξ, t) = ∑k0 i=1 ai(t)ξ i decay to zero algebraically as tk (λk = k/2) and the decay is even faster if the low Richardson moments vanish. The dynamics for global strong solutions are discussed as well.
منابع مشابه
Large-time rescaling behaviors for large data to the Hele-Shaw problem
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