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Abstract
Traveling wave solutions of reaction-diffusion systems have been studied to explain wave propagation phenomena in biological organisms. For population dynamics, there are two most frequently used reaction functions: KPP equation and Allen-Cahn equation. In this talk, we will look at how to construct a traveling wave solution by the shooting method and examine the differences between KPP and Allen-Cahn types. In particular, we focus on their physical implications, real-world examples for each type, and ways to improve current models. This talk also presents recent research on traveling wave solutions involving discontinuities, multistability and heterogeneity.
Brief Biography
Hoyoun Kim is currently working as a postdoctoral research fellow at CEMSE division at the King Abdullah University of Science and Technology (KAUST). He received a bachelor degree (2016) and master & Ph.D integrated degree (2022) in Mathematics from KAIST. He joined the Applied PDE group of AMCS in September 2022, and now he is working on hyperbolic and parabolic PDEs in Professor Tzavaras group, specially interested in diffusion theory and kinetic equations.