状态依赖时滞非局部扩散方程的波前解  

Traveling Wave Fronts for the Nonlocal Dispersal Equation with State-dependent Delay

作　　者：万育基 余志先 孟艳玲[3] Yu Ji WAN;Zhi Xian YU;Yan Ling MENG(College of Science, University of Shanghai for Science and Technology, Shanghai 200093, P. R. China;Mathematics and Science, College, Shanghai Normal University, Shanghai 200234, P. R. China;College of Science, University of Shanghai for Science and Technology, Shanghai 200093, P. R. China;Business School, University of Shanghai for Science and Technology, Shanghai 200093, P. R. China)

机构地区：[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

出　　处：《数学学报（中文版）》2019年第3期479-496,共18页Acta Mathematica Sinica：Chinese Series

基　　金：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.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.

关 键 词：波前解 非局部扩散 状态依赖时滞 SCHAUDER不动点定理 

分 类 号：O177.2[理学—数学]