Academic report on“Spreading Speeds Determinacy for a Cooperative Lotka-Volterra System with Stacked Fronts”

Academic report on“Spreading Speeds Determinacy for a Cooperative Lotka-Volterra System with Stacked Fronts”

At the invitation of Center for Mathematical Sciences and School of Mathematics and Physics, China University of Geosciences (Wuhan), on May 10, 2021, Professor Chunhua Ou (Memorial University of Newfoundland, Canada) conducted an online academic exchange with us and gave an academic presentation named “Spreading Speeds Determinacy for a Cooperative Lotka-Volterra System with Stacked Fronts”. This academic colloquium was hosted by Professor Shangjiang Guo.

This talk concerns the determinacy of invasion speed of each species for the cooperative Lotka-Volterra system, which admits single or multiple spreading speeds (co-speed or fast-slow speed). In the existence of a single spreading speed, the two species share a common invasion speed, and nonnegative traveling wave profiles connecting the extinction equilibrium exist if the wave speed is not less than the common speed. Predicting or determining the invasion speed can be linked to the linearized system at the extinction state. The existence of multiple spreading speeds indicates new connections of traveling wave profiles into certain intermediate states. Due to this, the determinacy of each spreading speed focuses not only on the extinction states but also on the corresponding intermediate states. Further, based on constructions of upper-lower solutions, they establish a criteria that can determine the fast-slow invasive speeds.

Professor Ou described the difficult mathematical problems vividly, which made the present teachers and students easily acceptant and deeply inspired. At the end of this colloquium, Professor Ou had a detailed discussion with relevant teachers and students. The lecture ended successfully in a warm atmosphere.