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| 状态依赖时滞非局部扩散方程的波前解 | |
| 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 |
| 作者姓名： | 万育基 余志先 孟艳玲 |
| 作者单位： | 1.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 |
| 基金项目： | 上海自然科学基金资助项目（18ZR1426500） |
| 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. |
| 关 键 词： | 波前解 非局部扩散 状态依赖时滞 Schauder不动点定理 |
Traveling Wave Fronts for the Nonlocal Dispersal Equation with State-dependent Delay |
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| Yu Ji WAN,Zhi Xian YU,Yan Ling MENG. Traveling Wave Fronts for the Nonlocal Dispersal Equation with State-dependent Delay[J]. Acta Mathematica Sinica, 2019, 62(3): 479-496 | |
| Authors: | Yu Ji WAN Zhi Xian YU Yan Ling MENG |
| Affiliation: | 1.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 |
| Abstract: | This paper is concerned with traveling waves for the nonlocal dispersal equation with the state-dependent delay. If the birth function is monotone, then the existence and nonexistence of monotone traveling waves are established. By a prior estimate and Ikehara's Theorem, we obtain the asymptotic behavior of critical traveling wave fronts. Finally, by introducing two auxiliary quasi-monotone equations, we improve our results of existence to the non-quasi-monotone equation. |
| Keywords: | traveling wave Fronts nonlocal dispersal state-dependent delay Schauder's fixed point theorem |
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