Diff. Geom, Math. Phys., PDE Seminar: Tuoc Van Phan

  • Date: 10/27/2015
  • Time: 15:30
Tuoc Van Phan, University of Tennessee, Knoxville

University of British Columbia


Gradient estimates and global existence of smooth solutions to a cross-diffusion system


We investigate the global time existence of smooth solutions for the Shigesada-Kawasaki-Teramoto system of cross-diffusion equations of two competing species in population dynamics. If there are self-diffusion in one species and no cross-diffusion in the other, we show that the system has a unique smooth solution for all time in bounded domains of any dimension. We obtain this result by deriving global W^{1,p}-estimates of Calder\'{o}n-Zygmund type  for a class of nonlinear reaction-diffusion equations with self-diffusion. These estimates are achieved by employing Caffarelli-Peral perturbation technique together with a new two-parameter scaling argument.


The talk is based on the joint work with L. Hoang (Texas Tech) and T. Nguyen (U. of Akron).

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Location: ESB 2012