### Spreading profile and nonlinear Stefan problems

Du, Y *(Univ of New England, Australia)*

Monday 23 June 2014, 16:00-16:30

Seminar Room 2, Newton Institute Gatehouse

#### Abstract

I will report some recent progresses (in joint works with Z. Guo, B. Lou, H. Matsuzawa, H. Matano, K. Wang, M. Zhou etc.) on the study of a general nonlinear Stefan problem, used as a model for the understanding of a variety of spreading phenomena, where the unknown function u(t,x) represents the density of concentration of a certain (chemical or biological) species at time t and space location x, with the free boundary standing for the spreading front. Such spreading problems are usually modeled by the corresponding Cauchy problem, which has attracted extensive research starting from the well-known 1937 paper of Kolmogorov-Petrovski-Piskunov. We will discuss the similarity and differences of the long-time behavior of these two types of mathematical models by closely examining their spreading profiles.

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