《山东大学学报(理学版)》 ›› 2024, Vol. 59 ›› Issue (6): 116-121, 126.doi: 10.6040/j.issn.1671-9352.0.2022.664
王彦平(
),李远飞*()
Yanping WANG(),Yuanfei LI*()
摘要：
考虑模拟阿尔茨海默(Alzheimer)病早期斑块形成的趋化系统，其模型定义在一个具有光滑边界的有界凸区域。假设系统的初始值满足一定的约束条件，推导解的先验估计。利用这些先验估计，证明趋化系统的解的连续依赖于方程中的参数。结果表明，方程中的参数的微小变化不会对系统造成巨大影响。
中图分类号:
| 1 |
LUCA M , CHAVEZ-ROSS A , EDELSTEIN-KESHET L , et al. Chemotactic signaling, microglia, and Alzheimer's disease senile plaques: is there a connection?[J]. Bulletin of Mathematical Biology, 2003, 65 (4): 693- 730.
doi: 10.1016/S0092-8240(03)00030-2 |
| 2 |
TAO Youshan , WANG Zhian . Competing effects of attraction vs. repulsion in chemotaxis[J]. Mathematical Models and Methods in Applied Sciences, 2013, 23 (1): 1- 36.
doi: 10.1142/S0218202512500443 |
| 3 |
JIN Haiyang , WANG Zhian . Asymptotic dynamics of the one-dimensional attraction-repulsion Keller-Segel model[J]. Mathematical Methods in the Applied Sciences, 2015, 38 (3): 444- 457.
doi: 10.1002/mma.3080 |
| 4 | LIU Jia , WANG Zhian . Classical solutions and steady states of an attraction-repulsion chemotaxis in one dimension[J]. Journal of Biological Dynamics, 2012, 6 (Suppl 1): 31- 41. |
| 5 |
LIU Dongmei , TAO Youshan . Global boundedness in a fully parabolic attraction-repulsion chemotaxis model[J]. Mathematical Methods in the Applied Sciences, 2015, 38 (12): 2537- 2546.
doi: 10.1002/mma.3240 |
| 6 |
JIN Haiyang . Boundedness of the attraction-repulsion Keller-Segel system[J]. Journal of Mathematical Analysis and Applications, 2015, 422 (2): 1463- 1478.
doi: 10.1016/j.jmaa.2014.09.049 |
| 7 |
LIN Ke , MU Chunlai , WANG Liangchen . Large-time behavior of an attraction-repulsion chemotaxis system[J]. Journal of Mathematical Analysis and Applications, 2015, 426 (1): 105- 124.
doi: 10.1016/j.jmaa.2014.12.052 |
| 8 | HIRSCH M W , SMALE S . Differential equations, dynamical systems and linear algebra[M]. New York: Academic Press, 1974. |
| 9 | LI Yuanfei , CHEN Xuejiao , SHI Jincheng . Structural stability in resonant penetrative convection in a Brinkman-Forchheimer fluid interfacing with a darcy fluid[J]. Applied Mathematics & Optimization, 2021, 84 (1): 979- 999. |
| 10 |
LIN C H , PAYNE L E . Continuous dependence on the Soret coefficient for double diffusive convection in Darcy flow[J]. Journal of Mathematical Analysis and Applications, 2008, 342 (1): 311- 325.
doi: 10.1016/j.jmaa.2007.11.036 |
| 11 | 李远飞, 肖胜中, 郭连红. 存在饱和蒸汽的大气原始方程组解对边界参数的收敛性[J]. 四川师范大学学报(自然科学版), 2021, 44 (5): 644- 653. |
| LI Yuanfei , XIAO Shengzhong , GUO Lianhong . The convergence of the primitive equations of the atmosphere in presence of vapour saturation on the boundary parameters[J]. Journal of Sichuan Normal University (Natural Science), 2021, 44 (5): 644- 653. | |
| 12 | 石金诚, 李远飞. 多孔介质中的Darcy方程组解的结构稳定性[J]. 浙江大学学报(理学版), 2021, 48 (3): 298- 303. |
| SHI Jincheng , LI Yuanfei . Structural stability of solutions for the Darcy equations in porous medium[J]. Journal of Zhejiang University (Science Edition), 2021, 48 (3): 298- 303. | |
| 13 | 李远飞, 郭战伟. Brinkman-Forchheimer流体与Darcy流体界面连接共振渗透[J]. 应用数学学报, 2021, 44 (2): 226- 237. |
| LI Yuanfei , GUO Zhanwei . Structural stability of a resonant penetrative convection in a Brinkman-Forchheimer fluid interfacing with a darcy fluid[J]. Acta Mathematicae Applicatae Sinica, 2021, 44 (2): 226- 237. | |
| 14 | LI Yuanfei , LIN Changhao . Continuous dependence for the nonhomogeneous Brinkman-Forchheimer equations in a semi-infinite pipe[J]. Applied Mathematics and Computation, 2014, 244, 201- 208. |
| 15 | PAYNE L E , SONG J C , STRAUGHAN B . Continuous dependence and convergence results for Brinkman and Forchheimer models with variable viscosity[J]. Proceedings of the Royal Society, 1999, 455, 2173- 2190. |
| 16 | GENTILE M , STRAUGHAN B . Structural stability in resonant penetrative convection in a Forchheimer porous material[J]. Nonlinear Analysis: Real World Applications, 2013, 14 (1): 397- 401. |
| [1] | 孙盼,张旭萍. 具有无穷时滞脉冲发展方程解的连续依赖性[J]. 《山东大学学报(理学版)》, 2023, 58(6): 77-83, 91. |
| [2] | 欧阳柏平,李远飞. 多孔介质中的一类流体方程组的连续依赖性[J]. 《山东大学学报(理学版)》, 2021, 56(2): 103-110. |
| [3] | 李远飞. 原始方程组对黏性系数的连续依赖性[J]. 《山东大学学报(理学版)》, 2019, 54(12): 12-23. |
| [4] | 席进华. 四阶两点常微分方程边值问题解的存在性[J]. J4, 2009, 44(1): 67-73 . |
| [5] | 肖 华 . 多维反射倒向随机微分方程的解对参数的连续依赖性[J]. J4, 2007, 42(2): 68-71 . |
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