MBI Publications

MBI Publications for Tong Li (3)

  • K. Zhao and T. Li
    Global existence and long-time behavior of entropy weak solutions to a quasilinear hyperbolic blood flow model
    Network and Heterogeneous MediaVol. 6, 2011 No. 4 (2011) pp. 625-646


    This paper is concerned with an initial-boundary value problem

    on bounded domains for a one dimensional quasilinear hyperbolic model of

    blood flow with viscous damping. It is shown that L1 entropy weak solutions

    exist globally in time when the initial data are large, rough and contains

    vacuum states. Furthermore, based on entropy principle and the theory of

    divergence measure field, it is shown that any L1 entropy weak solution converges

    to a constant equilibrium state exponentially fast as time goes to infinity.

    The physiological relevance of the theoretical results obtained in this paper is

  • T. Li, K. Zhao, R. Pan and R. Pan
    Global dynamics of a chemotaxis model on bounded
    SIAM Journal on Applied Mathematics (2012)


    We prove global existence and qualitative behavior of classical solutions for
    a hyperbolic-parabolic system describing chemotaxis on bounded domains. It is shown
    that classical solutions to the initial-boundary value problem of the one-dimensional
    model exist globally in time for large initial data and the solutions converge to constant
    equilibrium states exponentially in time, which rigorously demonstrates the collapsing of
    cell populations in chemotaxis. Moreover, similar results are established for the multi-
    dimensional model when the initial data are small.
  • T. Li, R. Pan and K. Zhao
    Global dynamics of a chemotaxis model on bounded domains with large data
    SIAM Journal on Applied MathematicsVol. 72 No. 1 (2012)


View Publications By