Asymptotic behavior of solutions to two-dimensional chemotaxis system with logistic source and singular sensitivity

作者：Cao, Junhong; Wang, Wei^*; Yu, Hao

来源：Journal of Mathematical Analysis and Applications, 2016, 436(1): 382-392.

DOI：10.1016/j.jmaa.2015.11.058

• Chemotaxis
• Asymptotic behavior
• Logistic source
• Singular sensitivity

In this paper we study the asymptotic behavior of solutions to the parabolic-elliptic chemotaxis system with singular sensitivity and logistic source: ut = Delta u - chi del . (u/v del v) + ru - mu u(2), 0 = Delta v - v + u, subject to homogeneous Neumann boundary conditions in a bounded domain Omega subset of R-2 with smooth boundary, where chi,mu > 0 and r is an element of R. It is proved that for any nonnegative initial date u(0) is an element of C ((Omega) over bar) such that integral(Omega), u(0)(-1) < 16 mu eta vertical bar Omega vertical bar(2)/chi(2) with the constant eta relying on Omega, the solution (u(.,t),v(.,t)) converges asymptotically to the constant equilibrium (r/mu, r/mu) in the L-infinity -norm as t -> infinity if r > 2(root chi + 1 - 1)(2) + chi(2)/(16 eta vertical bar Omega vertical bar).

• 出版日期2016-4-1
• 单位大连理工大学