Professor Yihong Du obtained his PhD in 1988 from Shandong University. After spending two years at Shandong University as a Lecturer (1988-90), and one year at Heriot-Watt University (UK) as a visiting fellow (1990-91), he joined University of New England in Australia in 1991, as a postdoctoral research fellow (1991-92) working with Prof. E.N. Dancer on an ARC supported project. Dr Du became a lecturer in 1993 and was promoted to a professor in 2008. He is interested in mathematical problems arising from applications in other sciences, such as biology, invasion ecology and chemical reaction theory. Some of his recent works investigate mathematical models for propagation, such as spreading of diseases, or invasion of exotic species, which involve nonlinear elliptic and parabolic equations, often with a free boundary to represent the propagation front. For research achievements in this and other areas, he was elected a Fellow of the Australian Academy of Science in 2021. In 2024, he was awarded an Australian Laureate Fellow by the Australian Research Council.
In this talk， I will report some recent progress on a free boundary model, where the free boundary conditions are deduced from the biological assumption that the species expands or shrinks its population range through its members at the range boundary keeping the population density there at a “preferred level”. It turns out that this strategy would make the species a super invader: no matter whether the growth function f(u) is monostable, bistable (strong Allee) or of combustion type (weak Allee), the species always spreads successfully.
