A quasilinear parabolic-elliptic chemotaxis-growth system with nonlinear secretion

作者：Zhao, Jie^*; Mu, Chunlai; Wang, Liangchen; Lin, Ke

来源：APPLICABLE ANALYSIS, 2020, 99(1): 86-102.

DOI：10.1080/00036811.2018.1489955

• Chemotaxis
• boundedness
• asymptotic behavior
• logistic source

This paper deals with the parabolic-elliptic chemotaxis-growth system with nonlinear secretion
u(t) = del center dot (D(u)del u) - del center dot (chi u del v) + au - bu(r), x is an element of Omega, t > 0,
0 = Delta v - v + u(k), x is an element of Omega, t > 0,
under homogeneous Neumann boundary conditions in a bounded domain Omega subset of R-n(n >= 2) with smooth boundary, where chi > 0, a > 0, b > 0, r > 1, k >= 1 and D(u) is a smooth function satisfying D(u) > c(D)u(m-1) with some c(D) > 0 and m >= 1. It is shown, either
r < k + 1, m > k + 1 - 2/n,
or
r > k + 1,
or
r = k + 1, b > b*, where
b* = {0, if m > k + 1 - 2/n,
n(k + 1 - m) - 2/n(k + 1 - m), if m <= k + 1 - 2/n,
then the system admits a unique global bounded classical solution. Moreover, we obtain the large time behavior of the solution for a specific logistic source. Finally, for the case D(u) = 1 and r = k+1, large time behavior and convergence rate are established.

• 出版日期2020-1-2
• 单位重庆大学