具有间接信号吸收和Logistic源的生物趋化模型解的有界性

Boundedness of Solution for the Chemotaxis Model with Indirect Signal Absorption and Logistic Source

本文考虑具有二维间接信号吸收的拟线性趋化模型:其中Ω∈Rn(n=2)是一个有界区域且具有光滑边界,μ,l】0,非线性扩散系数D(u)和趋化敏感系数S(u)分别满足D(u)≥(u+1)m-1,S(u)≤(u+1)q-1且D(⋅),S(⋅)∈C1+l([0,∞))。本文利用能量方法和半群理论证明在和0 C,λ0为正常数。

In this paper, we consider the following two-dimensional quasilinear chemotaxis model with in-direct signal absorption: on a bounded domain Ω∈Rn(n=2), with smooth boundary , μ and l are positive constants, the nonlinear diffusivity D(u) and chemosensitivity S(u) are supposed to satisfy D(u)≥(u+1)m-1, S(u)≤(u+1)q-1 and D(⋅),S(⋅)∈C1+l([0,∞)). Finally, we use the energy method and the semigroup theory to prove that the solution of the biologicalchemotaxis model is globally bounded under the conditions and 0 C,λ0 are the positive constants.