Time: 16:00-18:00 PM, Oct. 30^th, 2021.

Venue: C302B Mingli Building

This lecture deals with a general cross-diffusion system modeling the dynamics behavior of two predators and one prey with signal-dependent diffusion and sensitivity subject to homogeneous Neumann boundary conditions. Firstly, in light of some L^p-estimate techniques, we rigorously prove the global existence and uniform boundedness of positive classical solutions in any dimensions with suitable conditions on motility functions and the coefficients of logistic source. Moreover, by constructing some appropriate Lyapunov functionals, we further establish the asymptotic behavior of solutions to a specific model with Lotka-Volterra type functional responses and density-dependent death rates for two predators as well as logistic type for the prey. Our results not only generalize the previously known one, but also present some new conclusions.

Bio

Professor Mu Chunlai is the New Century Excellent Talent of the Ministry of Education, the head of the National First-Class Major, the municipal academic technology leader, and the Vice Chairman of the Municipal Mathematics Society. He was awarded the 2^ndPrize of Natural Science Award of Ministry of Education in 2019, the 2^ndPrize of Chongqing Self-Science Award in 2016 and the 2^ndprize of National Teaching Achievement in 2014. He undertakes more than 20 scientific projects such as National Self-Science Fund and Municipal Key Fund. He is engaged in the research of nonlinear partial differential equations and biomathematics, and has published more than 200 papers in authoritative journals such asM3AS,J. Diff.eq.,J. sci. comput.

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Organizer and sponsor:Scientific Research Department

School of Sciences

Artificial Intelligence Institute