Research at FAST

84 Department of Applied Mathematics Department of Applied Mathematics Qualification MSc (HIT) PhD (HIT) 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. We are interested in the interactions between solitons and their global behavior. 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 behavior 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 nature method used to calculate the solutions to the kinetic equations. Representative Publications • Y. Gao and H. Liu, Global N-peakon weak solutions to a family of nonlinear equations, J. Differential Equations, ( 2021 ), 271: 343-355 • Y. Gao , Yuan Gao and Jian-Guo Liu, Large time behavior, bi-Hamiltonian structure and kinetic formulation for complex Burgers equation, ( 2020 ), Quart. Appl. Math. • Y. Gao , L. Li and J.-G. Liu, Patched peakon weak solutions of the modified Camassa-Holm equation, Physica D, ( 2019 ), 390: 15-35 • Y. Gao , L. Li and J.-G. Liu, A dispersive regularization for the modified Camassa-Holm equation, SIAM J. Math. Anal., ( 2018 ), 50(3):2807-2838 • Y. Gao and J.-G. Liu, The modified Camassa-Holm equation in Lagrangian coordinates, Discrete Contin. Dyn. Syst. Ser. B., ( 2018 ), 23(6):2545-2592 • Y. Gao and X. Xue, Global existence and uniqueness of measure valued solutions to a Vlasov type equation with local alignment, Math. Methods Appl. Sci. ( 2017 ), 40:7640-7662 • Y. Gao and J.-G. Liu, Global convergence of a sticky particle method for the modified Camassa-Holm equation, SIAM J. Math. Anal., ( 2017 ), 49(2):1267-1294 Awards • 2019 Excellent Doctoral Thesis (HIT) • 2018 Gold Medal of Doctoral Thesis for New World Mathematics Awards