一类带反应项的 Othmer-Stevens型趋化模型解的存在性

该文讨论了一类带反应项的Othmer-Stevens 型趋化模型的初边值问题{∂u/∂t=D∨(u∨lnu/Φ(x, t, w))+ f(x, t, u),∂w/∂t=g(x, t, u, w),u∨lnu/Φ(x, t, w) ?n^→=0.证明了: 如果边界∂Ω ∈C^2+β, 函数Φ(x, t , w), f(x, t, u) 和 g(x, t, u, w)充分光滑,则该系统存在唯一解.

Existence of Solution to Some Othmer-Stevens Chemotaxis System with Reaction Term

In this paper, the authors study an initial-boundary value problem of Othmer-Stevens chemotaxis system with reaction term in the master equation{∂u/∂t=D∨(u ∨ln u/Φ(x, t, w))+ f(x, t, u),  ∂w/∂t=g(x, t, u, w), u∨ln u/Φ(x, t, w) ?n^→=0.They prove that there exists a unique solution if the boundary ∂Ω ∈^C2+β, the functions Φ(x, t, w), f(x, t, u) and g(x, t, u, w) are  sufficiently smooth.