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
DOI: 10.12677/PM.2021.113048, PDF,    科研立项经费支持
作者: 刘璐璐, 辛 巧*：伊犁师范大学数学与统计分院，新疆 伊宁
关键词: 间接信号吸收；拟线性；趋化；Logistic源；有界性；Indirect Signal Absorption； Quasilinear； Chemotaxis； Logistic Source； Boundednes
摘要: 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 < q ≤ 2的条件下，该生物趋化模型的解全局有界，其中C,λ0为正常数。
Abstract: 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 < q ≤ 2, where C,λ0 are the positive constants.
文章引用：刘璐璐, 辛巧. 具有间接信号吸收和Logistic源的生物趋化模型解的有界性[J]. 理论数学, 2021, 11(3): 362-370. https://doi.org/10.12677/PM.2021.113048

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