Critical Thresholds, Entropy and Structure-preserving Algorithms
Student No.:40
Time:Mon & Wed 13:30-15:05, May.16-29
Instructor:Liu Hailiang  
Place:Conference Room 1, Jin Chun Yuan West Bldg.
Starting Date:2018-5-16
Ending Date:2018-5-29

The course discusses intrinsic solution properties for several time-dependent problems, described by nonlinear partial differential equations balanced with diffusion, convection, and various interactions. Topics studied in this course will be on the interplay between analytical theory and computational aspects of structure-preserving algorithms with real applications. Here is an outline of the main topics: (1) Critical thresholds; (2) Transport equations in biology and entropy, and  (3) Structure-preserving approximations for diffusion with drifts.


Prerequisite: Differential equations



[1] Mathematical models in Biology: Benoit Perthame, Transport equations in Biology, Birkaeuser Verlag, 2007.
[2] Critical threshold phenomena: S. Engelberg, H. Liu and E. Tadmor, Critical threshold phenomena in Euler-Poisson equations , Indiana University Mathematics Journal, 50 (1) (2001), 109--157.
[3] Direct Discontinuous Galerkin methods: H. Liu and J. Yan, The Direct Discontinuous Galerkin (DDG) method for diffusion with interface corrections, Commun. Comput. Phys. 8(3) (2010), 541--564.