大象传媒

听

Speaker: Dr.听Yu-Lin Lin听(Institute of Mathematics, Academia Sinica, Taipei, Taiwan)

Title: "Large-time rescaling behaviors to the Hele-Shaw problem driven by听injection"

Abstract:听This talk addresses a large-time rescaling behavior of Hele-Shaw cells听for large 听data initial domains. The Polubarinova-Galin equation is the听reformulation of zero surface tension Hele-Shaw flows with injection at听the origin in two dimensions by considering the moving domain听$\Omega(t)=f(B_{1}(0),t)$ for some Riemann mapping f(z,t). We give a听sharp large-time rescaling behavior of global strong polynomial听solutions to this equation and the corresponding moving boundary in听terms of the invariant complex moments. Furthermore, by proving a听perturbation theorem of polynomial solutions, we also show that a small听perturbation of the initial function of a global strong polynomial听solution also gives rise to global strong solution and a large-time听rescaling behavior of the 听moving domain is shown as well.

Information on听previous seminars听can be found听here.