DEPARTMENT OF APPLIED MATHEMATICS 76 Email mathyu.gao@polyu.edu.hk Qualification BSc (Harbin Institute of Technology) PhD (Harbin Institute of Technology) ORCID ID 0000-0002-8535-3889 Dr GAO Yu Research Assistant Professor Research Overview My research interest lies in nonlinear partial differential equations, especially nonlinear dispersive equations and kinetic equations. The equations we studied come from physics and biology. For the dispersive equations, they are used to describe shallow water waves. One of the most important types of shallow water waves is known as soliton waves. Our group is interested in the interactions between solitons and their global behaviour. We used global multi-solitons to construct general global weak solutions to some dispersive equations. The kinetic equations we studied come from statistical mechanics and some models describing the emergent behaviour of a flock of birds, a swarm of bacteria or a school of fish. When the number of agents goes to infinity, it is more convenient to use a kinetic equation to describe the density of the group of agents. Particle method is a natural method used to calculate the solutions to the kinetic equations. Representative Publications • J. Math. Phys., 2022, 63(12), 121503 • SIAM J. Math. Anal., 2022, 54(1), 423-452 • J. Math. Anal. Appl., 2022, 515(2), 126428 • Discrete Contin. Dyn. Syst. Ser. B., 2022, 27(8): 4317-4329 • J. Differential Equations, 2021, 271:343-355 • Quart. Appl. Math., 2021, 79:55-102
RkJQdWJsaXNoZXIy Mjc5OTU=