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程红梅
职 称：副教授 硕士生导师
办公室：长清湖校区文渊楼B511
邮 箱：hmcheng@sdnu.edu.cn
个人简介
程红梅，女，数学博士，副教授，硕士生导师。近年来一直致力于对带有非局部扩散项和时滞的反应扩散方程在受到环境影响时解的定性行为的变化和特殊平衡解---强迫行波解的存在性及其稳定性的研究,发表学术论文十余篇，主持国家级项目一项，省部级项目一项。
研究兴趣
非局部反应扩散方程行波解；分数阶反应扩散方程
招生方向
硕士研究生招生专业：应用数学
开设课程
高等数学；反应扩散方程
科研项目
1.山东省博士基金，ZR2017BA005，分数阶反应扩散方程行波解的存在性和定性性质，2017/08-2019/12，主持
2.国家青年自然科学基金, 11701341，非局部反应扩散方程行波解的存在性和定性分析, 2018/01-2020/12, 主持
代表性成果
1. Qingru Guo and Hongmei Cheng, Existence of forced waves and their asymptotics for Leslie-Gower prey-predator model with some shifting environments, Discrete Contin. Dyn. Syst. Ser. B，29(5)(2024), 2419-2434.
2. Qinhe Fang, Hongmei Cheng and Rong Yuan, Spatial dynamics of some modified Leslie-Gower prey-predator model with shifting habitat, J. Math. Anal. Appl., 518(2)(2023), 126713.
3. Qinhe Fang, Hongmei Cheng and Rong Yuan, Spatial dynamics of a nonlocal dispersal Leslie-Gower predator-prey model with some shifting habitats, Discrete and Continuous Dynamical Systems, 43(8)(2023), 2985-3007.
4. Yang Xia, Hongmei Cheng and Rong Yuan, A free boundary problem of some modified Leslie-Gower predator-prey model with shifting environment, Journal of Applied Analysis and Computation, 1(6)(2022), 2396-2425.
5. Hongmei Cheng, Qinhe Fang and Yang Xia, A free boundary problem for some modified predator-prey model in a higher dimensional environment, Appl. Math., 67(5) (2022), 615-632.
6. Shiwen Niu, Hongmei Cheng and Rong Yuan, A free boundary problem of some modified Leslie-Gower predator-prey model with nonlocal diffusion term, Discrete Contin. Dyn. Syst. Ser B, 27(4)(2022), 2189-2219.
7. Hongmei Cheng and Rong Yuan, The stability of traveling waves for Allen-Cahn equations with fractional Laplacian, Appl. Anal., 101(1)(2022), 263-273.
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