In this talk, I shall report some recent progress on the existence and multiplicity of traveling waves to some of the most important models in Turing Pattern Formation and Ecology. In addition, I shall pose some open questions which are wide open and demand new ideas and fresh approaches.
Professor Yuanwei Qi (University of Central Florida) graduated from the Department of Mathematics of Peking University in 1982, received a master's degree from the Chinese Academy of Sciences in 1985, a doctorate from Oxford University in1990, and taught at the Hong Kong University of Science and Technology and UC Santa Barbarra. He also served as a professor of the 100-person program in Shanxi Province at Shanxi University. Professor Qi is an international expert on the direction of influential partial differential equations. Since 1994, he has conducted academic exchanges in Oxford University, British Columbia University, Chinese Academy of Sciences, Tsinghua University and other schools and scientific research institutions. Since 1998, he has been invited to make an invitation report at the World Academic Conference more than 20 times. He has published more than 30 high-level academic papers in the internationally renowned Journal such as SIAM J. Math. Anal., SIAM J. Appl. Math., J. Differential Equations, Discrete Contin. Dyn. Syst., etc.