状态依赖时滞非局部扩散方程的波前解

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状态依赖时滞非局部扩散方程的波前解万育基¹, 余志先^1,2, 孟艳玲³1 上海理工大学理学院上海 200093;
2 上海师范大学数理学院上海 200234;
3 上海理工大学管理学院上海 200093 Traveling Wave Fronts for the Nonlocal Dispersal Equation with State-dependent Delay Yu Ji WAN¹, Zhi Xian YU^1,2, Yan Ling MENG³1 College of Science, University of Shanghai for Science and Technology, Shanghai 200093, P. R. China;
2 Mathematics and Science, College, Shanghai Normal University, Shanghai 200234, P. R. China;
3 usiness School, University of Shanghai for Science and Technology, Shanghai 200093, P. R. China

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摘要本文主要研究状态依赖时滞非局部扩散方程的波前解，当出生函数单调时，可以得到单调行波解的存在性和非存在性，然后，由先验估计和Ikehara定理，进一步得到临界波前解的渐近性；当出生函数非单调时，通过引进两个辅助拟单调方程，也可以得到相应非拟单调条件下的存在性结果.

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收稿日期: 2018-06-19

MR (2010):

O177.2

基金资助:上海自然科学基金资助项目（18ZR1426500）

通讯作者:余志先E-mail: zxyu0902@163.com

作者简介: 万育基,E-mail:yjwan0530@163.com;孟艳玲,E-mail:ylmeng0321@163.com

引用本文:

万育基, 余志先, 孟艳玲. 状态依赖时滞非局部扩散方程的波前解[J]. 数学学报, 2019, 62(3): 479-496. Yu Ji WAN, Zhi Xian YU, Yan Ling MENG. Traveling Wave Fronts for the Nonlocal Dispersal Equation with State-dependent Delay. Acta Mathematica Sinica, Chinese Series, 2019, 62(3): 479-496.

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