具有奇异灵敏度的趋化模型解的有界性  

Boundedness of Solutions for Chemotaxis Model with Singular Sensitivity

作　　者：杨兰 李中平[2] YANG Lan;LI Zhong-ping(School of Mathematical Sciences,University of Electronic Science and Technology of China,Chengdu Sichuan 611731,China;School of Mathematics and Information,China West Normal University,Nanchong Sichuan 637009,China)

机构地区：[1]电子科技大学数学科学学院,成都611731 [2]西华师范大学数学与信息学院,四川南充637009

出　　处：《西华师范大学学报（自然科学版）》2024年第6期600-605,共6页Journal of China West Normal University(Natural Sciences)

基　　金：四川省中央引导地方科技发展专项(2022ZYD0007)。

摘　　要：在齐次Neumann边界条件下,考虑了具有奇异灵敏度和间接信号产生机制的抛物-抛物-ODE趋化模型。当模型中的参数满足一定的条件时,已有文献给出解的整体存在性,而解的一致有界性尚未可知。因此,文中给出该模型解的一致有界性的严格证明。利用该模型已有解的第二个分量的一致下界估计,再运用Young不等式、Gagliardo-Nirenberg不等式、插值不等式等工具得到解的整体存在性和一致有界性的充分条件。This paper talks about a parabolic-parabolic-ODE chemotaxis model with singular sensitivity and indirect signal production mechanism under homogeneous Neumann boundary conditions.Previous literature showed the global existence of the solutions when the parameters in this model satisfy certain conditions.Howeves,the uniform boundedness of solutions is unknown.In this paper,the uniform boundedness of the solutions is further considered.The sufficient conditions for the global existence and uniform boundedness of the solutions can be obtained by employing the uniform lower bound estimate of the second solution component,Young inequality,Gagliardo-Nirenberg inequality and interpolation inequality.

关 键 词：整体存在性 一致有界性 趋化 奇异灵敏度 间接信号产生 

分 类 号：O175.26[理学—数学]