BOUNDEDNESS IN A CHEMOTAXIS SYSTEM WITH CONSUMPTION OF CHEMOATTRACTANT AND LOGISTIC SOURCE

作者：Wang Liangchen^*; Khan Shahab Ud Din; Khan Salah Ud Din

来源：Electronic Journal of Differential Equations, 2013, 209.

• Chemotaxis
• global existence
• boundedness
• logistic source

In this article, we consider a chemotaxis system with consumption of chemoattractant and logistic source %26lt;br%26gt;u(t) = Delta u - chi del . (u del v) + f(u), x is an element of Omega, t %26gt; 0, %26lt;br%26gt;v(t) = Delta v - uv, x is an element of Omega, t %26gt; 0, %26lt;br%26gt;under homogeneous Neumann boundary conditions in a smooth bounded domain Omega subset of R-n, with non-negative initial data u(0) and v(0) satisfying (u(0), v(0)) is an element of (W-1,W-theta(Omega))(2) (for some theta %26gt; n). chi %26gt; 0 is a parameter referred to as chemosensitivity and f(s) is assumed to generalize the logistic function %26lt;br%26gt;f(s) = as - bs(2), s %26gt;= 0, with a %26gt; 0, b %26gt; 0. %26lt;br%26gt;It is proved that if parallel to v(0)parallel to(L infinity(Omega)) %26gt; 0 is sufficiently small then the corresponding initial-boundary value problem possesses a unique global classical solution that is uniformly bounded.

• 出版日期2013-9-19
• 单位重庆大学