高维空间中具有间接信号产出生物趋化模型解的全局有界性
Global Boundedness of Classical Solutions to a High-Dimensional Chemotaxis Model with Indirect Signal Production
DOI: 10.12677/AAM.2019.84088, PDF,    科研立项经费支持
作者: 张冬冬, 辛 巧, 汤建钢：伊犁师范大学数学与统计分院，新疆 伊宁
关键词: 趋化性；全局存在性；有界性；间接信号产出；Chemoaxis； Globl Existence； Boundedness； Indirect Signal Production
摘要: 考虑一个高维空间中描述具有间接信号产出的山地松甲虫扩散和聚集模型 在齐次Neumann初值边界和非负初值条件下经典解的整体性态。假设是一个光滑有界区域，表示趋化敏感函数且满足，消耗函数为，Logistic源满足，是正的参数。先利用能量估计方法及Gagliardo-Nirenberg不等式建立u和w的先验估计，再运用Moser迭代证明了此问题存在经典解且一致有界，不存在坍塌现象。
Abstract: This paper deals with the chemotaxis system of diffusion and aggregation of Mountain Pine Beetle with indirect attractant production and generalized logistic source in a smoothly bounded domain with homoge-neous Neumann boundary conditions and nonnegative initial values, the chemotactic sensitivity function satisfies the consumption function and the logistic source satisfies Moreover, are given positive parameter. Firstly, the energy estimation method and Gagliardo-Nirenberg inequality are used to establish the local prior estimate of u and w, and then Moser iteration is used. This problem admits a unique global classical solution that is uniformly in-time bounded.
文章引用：张冬冬, 辛巧, 汤建钢. 高维空间中具有间接信号产出生物趋化模型解的全局有界性[J]. 应用数学进展, 2019, 8(4): 780-789. https://doi.org/10.12677/AAM.2019.84088

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