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

研究方向：常微分方程与动力系统

个人简介

程红梅，女，群众，1987年生，数学博士，副教授，硕士生导师。近年来致力于非局部反应扩散方程和分数阶反应扩散方程理论及应用方面的研究，获得一批应用基础性研究成果。在国际权威期刊发表SCI收录论文8篇。主持国家级科研项目1项，省部级科研项目1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；数学物理方程；偏微分方程；脉冲微分方程

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.H. Cheng and R. Yuan, The stability of the equilibria of the Allen-Cahn equation with fractional diffusion, Appl. Anal., 38(9)2019,600-610.

2.H. Cheng and R. Yuan, Traveling waves of some Holling-Tanner predator-prey system with nonlocal diffusion. Appl. Math. Comput.,338(1)2018,12-24.

3.H. Cheng and R. Yuan, Existence and stability of traveling waves for Leslie-Gower predator-prey system with nonlocal diffusion. Discrete Contin. Dyn. Syst. Ser. A, 2017,37:5433–5454.

4. H. Cheng and R. Yuan, Traveling waves of a nonlocal dispersal Kermack-McKerndrick epidemic model with delayed transmission, J.Evolution Equation,2017, 17:979-1002.

5. H. Cheng and R. Yuan, Existence and asymptotic stability of traveling fronts for nonlocal monostable evolution equations. Discrete Contin. Dyn. Syst. Ser. B, 2017, 22:3007–3022.

6. H. Cheng and R. Yuan, Stability of traveling wave fronts for nonlocal diffusion equation with delayed nonlocal response，Taiwanese J. Math., 2016, 20:801-822.

7. H. Cheng and R. Yuan, Multidimensional stability of disturbed pyramidal traveling fronts in the Allen-Cahn equation, Discrete Contin. Dyn. Syst. Ser. B, 2015, 20:1015-1029.

8. H. Cheng and R. Yuan, The spreading property for a prey-predator reaction-diffusion system with fractional diffusion, Frac. Calc. Appl. Anal., 2015, 18:565-579.