Well-posedness for a model derived from an attraction-repulsion chemotaxis system

作者：Shi, Renkun; Wang, Weike^*

来源：Journal of Mathematical Analysis and Applications, 2015, 423(1): 497-520.

DOI：10.1016/j.jmaa.20.14.10.006

• Chemotaxis
• Attraction-repulsion
• Half-order derivative
• Decay rate
• Blow-up

In this paper, we are interested in a model derived from an attraction-repulsion chemotaxis system in high dimensions:
{partial derivative(t)u - Delta u = -beta(1) Delta .(u del v) beta V-2 . (u del w), x is an element of R-n, t > 0, lambda(1)v - Delta v= u, x is an element of R-n, t > 0, lambda(2)w - Delta w= u, x is an element of R-n, t > 0, u(x, o)=u0(x), x is an element of R-n,
with the parameters beta(1) >= 0, beta(2) >= 0, lambda(1) > 0, lambda(2) > 0 and nonnegative initial data u0(x) is an element of L-1 (R-n) boolean AND L-infinity (R-n). We prove that a global bounded solution exists when the repulsion prevails over the attraction in the sense of beta(1) > beta(2). Moreover, we give the smoothness of the solution and obtain its decay rates in W-s,W-P(R-n), which coincide with the ones of the classical heat equation. Conversely, when n = 2, beta(1) > beta(2), we prove that the finite time blow-up may occur.

• 出版日期2015-3-1
• 单位上海交通大学