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(Jan. 20) Effects of density-suppressed motility in a chemotaxis-haptotaxis reaction-diffusion system

Last updated :2019-01-18

Topic: Effects of density-suppressed motility in a chemotaxis-haptotaxis reaction-diffusion system
Speaker: Professor MU Chunlai
(Chongqing University)
Time: 17:00-18:00, Sunday, January 20, 2019
Venue: Room 415, New Mathematics Building, Guangzhou South Campus, SYSU

Abstract:
This talk deals with the Neumann problem for the density-suppressed motility parabolic-parabolic-ODE chemotaxis-haptotaxis model of cancer invasion, which was initially proposed by Chaplain and Lolas (2006) to describe the interactions between cancer cells, the matrix degrading enzyme and the host tissue in a process of cancer cell invasion of tissue (extracellular matrix). The density-suppressed motility mechanism can induce spatiotemporal pattern formation through self-trapping with the parameters are positive. By treating the motility function as a weight function and employing the method of weighted energy estimates, we derive the L^1􀀀bound f v to rule out the degeneracy and that the system admits a unique global classical solution which is uniformly bounded in time in the two-dimensional spatial setting.

Furthermore, it is also shown that the system also possesses a unique classical solution for appropriately small initial data in the case of three-dimensional spatial domain. Finally, we also obtain that the constant steady state (1; 1; 0) is globally asymptotically stable.