Smoothness and Long-time Behavior of the Free Boundary in a Nonlinear Stefan Problem
Thursday, November 8, 2012 - 10:30am - 12:00pm
Yihong Du (University of New England)
We consider a nonlinear Stefan problem, which may be used to describe the spreading of invasive species, with the free boundary representing the invasing front. In one space dimension and in the radially symmetric case with a logistic nonlinear term, it is known that this model exhibits a spreading-vanishing dichotomy. In this talk we discuss the non-radially symmetric case. By establishing suitable regularity of the free boundary, we show that the spreading-vanishing dichotomy still holds. Moreover, when spreading happens, the normalized free boundary approaches the unit sphere as time goes to infinity, and the spreading speed is the same as in the radially symmetric case. This is joint work with Hiroshi Matano (Univ of Tokyo) and Kelei Wang (Wuhan Inst of Physics and Math).