移动环境下带有非局部扩散项和时滞的反应扩散方程的强迫行波解

数学物理学报 ›› 2022, Vol. 42 ›› Issue (2): 491-501.

移动环境下带有非局部扩散项和时滞的反应扩散方程的强迫行波解

程红梅^1,*(),袁荣²()

¹ 山东师范大学数学与统计学院济南 250358
² 北京师范大学数学与统计学院北京 100875

收稿日期:2021-05-12 出版日期:2022-04-26 发布日期:2022-04-18
通讯作者: 程红梅 E-mail:hmcheng@sdnu.edu.cn;ryuan@bnu.edu.cn
作者简介:袁荣, E-mail: ryuan@bnu.edu.cn
基金资助:
国家自然科学基金(11701341);国家自然科学基金(11771044)

Forced Waves of a Delayed Reaction-Diffusion Equation with Nonlocal Diffusion Under Shifting Environment

Hongmei Cheng^1,*(),Rong Yuan²()

¹ School of Mathematics and Statistics, Shandong Normal University, Jinan 250358
² School of Mathematical Sciences, Beijing Normal University, Beijing 100875

Received:2021-05-12 Online:2022-04-26 Published:2022-04-18
Contact: Hongmei Cheng E-mail:hmcheng@sdnu.edu.cn;ryuan@bnu.edu.cn
Supported by:
the NSFC(11701341);the NSFC(11771044)

摘要/Abstract

摘要：

该文考虑了移动环境下带有非局部扩散项和时滞的反应扩散方程的强迫行波解的存在性和唯一性. 首先利用上下解方法和单调迭代原理得到强迫行波解的存在性, 其中, 该强迫行波解以环境移动的速度来变化. 其次, 该文结合最大值原理, 利用挤压方法得到了该强迫行波解的唯一性. 最后, 作为该文得到的结论的应用, 该文给出了两个经典的模型, 一个是带非局部扩散项和时滞的Logistic模型, 另一个是带有非局部扩散项和时滞的quasi-Nicholson's Blowfiles人口模型.

关键词: 强迫行波解, 时滞反应扩散方程, 非局部扩散项, 移动环境.

Abstract:

This paper is devoted to establish the existence and uniqueness of the forced waves for a general reaction-diffusion equation with time delay and nonlocal diffusion term in a shifting environment. We first obtain the existence of the forced waves with the speed at which the habitat is shifting by using super- and sub-solutions method and monotone iteration method. Then we will give the uniqueness by applying the sliding method with the strong maximum principle. Finally, these analytical conclusions are applied to the nonlocal delayed Logistic model and the nonlocal delayed quasi-Nicholson's Blowfiles population model.

Key words: Forced waves, Delayed reaction-diffusion equation, Nonlocal diffusion, Shifting environment

中图分类号:

O175.2

程红梅,袁荣. 移动环境下带有非局部扩散项和时滞的反应扩散方程的强迫行波解[J]. 数学物理学报, 2022, 42(2): 491-501.

Hongmei Cheng,Rong Yuan. Forced Waves of a Delayed Reaction-Diffusion Equation with Nonlocal Diffusion Under Shifting Environment[J]. Acta mathematica scientia,Series A, 2022, 42(2): 491-501.

参考文献 29

1	Alfaro M , Berestycki H , Raoul G . The effect of climate shift on a species submitted to dispersion, evolution, growth and nonlocal competition. SIAM J Math Anal, 2017, 49 (1): 562- 596 doi: 10.1137/16M1075934
2	Bates P W , Fife P C , Ren X , Wang X . Traveling waves in a convolution model for phase transitions. Arch Rational Mech Anal, 1997, 138 (2): 105- 136 doi: 10.1007/s002050050037
3	Berestycki H , Diekmann O , Nagelkerke C , Zegeling P . Can a species keep pace with a shifting climate?. Bull Math Biol, 2009, 71: 399- 429 doi: 10.1007/s11538-008-9367-5
4	Berestycki H , Fang J . Forced waves of the Fisher-KPP equation in a shifting environment. J Differential Equations, 2018, 264 (3): 2157- 2183 doi: 10.1016/j.jde.2017.10.016
5	Berestycki H , Rossi L . Reaction-diffusion equations for population dynamics with forced speed I-The case of the whole space. Discrete Contin Dyn Syst, 2008, 21: 41- 67 doi: 10.3934/dcds.2008.21.41
6	Berestycki H , Rossi L . Reaction-diffusion equations for population dynamics with forced speed Ⅱ-Cylindrical-type domains. Discrete Contin Dyn Syst, 2009, 25: 19- 61 doi: 10.3934/dcds.2009.25.19
7	Carr J , Chmaj A . Uniqueness of travelling waves for nonlocal monostable equations. Proc Amer Math Soc, 2004, 132: 2433- 2439 doi: 10.1090/S0002-9939-04-07432-5
8	Chen X . Existence, uniqueness, and asymptotic stability of traveling waves in nonlocal evolution equations. Adv Differential Equations, 1997, 2 (1): 125- 160
9	Cheng H , Yuan R . Stability of traveling wave fronts for nonlocal diffusion equation with delayed nonlocal response. Taiwanese J Math, 2016, 20: 801- 822
10	Cheng H , Yuan R . Existence and asymptotic stability of traveling fronts for nonlocal monostable evolution equations. Discrete Contin Dyn Syst, 2017, 22 (7): 3007- 3022
11	Cheng H , Yuan R . Existence and stability of traveling waves for Leslie-Gower predator-prey system with nonlocal diffusion. Discrete Contin Dyn Syst, 2017, 37 (10): 5422- 5454
12	Cheng H , Yuan R . Traveling waves of a nonlocal dispersal Kermack-McKendrick epidemic model with delayed transmission. J Evol Equ, 2017, 17: 979- 1002 doi: 10.1007/s00028-016-0362-2
13	Cheng H , Yuan R . Traveling waves of some Holling-Tanner predator-prey system with nonlocal diffusion. Appl Math Comput, 2018, 338 (1): 12- 24
14	Coville J , Dupaigne L . Propagation speed of travelling fronts in non local reaction-diffusion equations. Nonlinear Anal, 2005, 60 (5): 797- 819 doi: 10.1016/j.na.2003.10.030
15	Coville J , Dupaigne L . On a non-local equation arising in population dynamics. Proc Roy Soc Edinburgh Sect A, 2007, 137 (4): 727- 755 doi: 10.1017/S0308210504000721
16	Fang J , Lou Y , Wu J . Can pathogen spread keep pace with its host invasion?. SIAM J Appl Math, 2016, 76 (4): 1633- 1657 doi: 10.1137/15M1029564
17	Hu H , Yi T , Zou X . On spatial-temporal dynamics of a Fisher-KPP equation with a shifting environment. Proc Amer Math Soc, 2020, 148 (1): 113- 221
18	Hu H , Zou X . Existence of an extinction wave in the Fisher equation with a shifting habitat. Proc Amer Math Soc, 2017, 145 (11): 4763- 4771 doi: 10.1090/proc/13687
19	Hutson V , Grinfeld M . Non-local dispersal and bistability. European J Appl Math, 2006, 17 (2): 221- 232 doi: 10.1017/S0956792506006462
20	Hutson V , Shen W , Vickers G . Spectral theory for nonlocal dispersal with periodic or almost-periodic time dependence. Rocky Mountain J Math, 2008, 38 (4): 1147- 1175
21	Li B , Bewick S , Shang J , Fagan W F . Persistence and spread of a species with a shifting habitat edge. SIAM J Appl Math, 2014, 74 (5): 1397- 1417 doi: 10.1137/130938463
22	Li W , Wang J , Zhao X . Spatial dynamics of a nonlocal dispersal population model in a shifting environment. J Nonlinear Sci, 2018, 28 (4): 1189- 1219 doi: 10.1007/s00332-018-9445-2
23	Murray J D. Mathematical Biology. Ⅱ: Spatial Models and Biomedical Applications. New York: Springer-Verlag, 2003
24	Van Der Waals J D. On the continuity of the gaseous and liquid states. Translated from the Dutch. Edited and with an introduction by Rowlinson J S. Studies in Statistical Mechanics. Amsterdam: North-Holland Publishing Co, 1988
25	Vo H H . Persistence versus extinction under a climate change in mixed environments. J Differential Equations, 2015, 259 (10): 4947- 4988 doi: 10.1016/j.jde.2015.06.014
26	Wang J , Zhao X . Uniqueness and global stability of forced waves in a shifting environment. Proc Amer Math Soc, 2019, 147: 1467- 1481
27	Wu C , Yang Y , Wu Z . Existence and uniqueness of forced waves in a delayed reaction-diffusion equation in a shifting environment. Nonlinear Analysis: Real World Applications, 2021, 57: 103198 doi: 10.1016/j.nonrwa.2020.103198
28	Wu J , Zou X . Traveling wave fronts of reaction-diffusion systems with delay. J Dynam Differential Equations, 2001, 13 (3): 651- 687 doi: 10.1023/A:1016690424892
29	Zhang G , Zhao X . Propagation dynamics of a nonlocal dispersal Fisher-KPP equation in a time-periodic shifting habitat. J Differential Equations, 2020, 268 (6): 2852- 2885 doi: 10.1016/j.jde.2019.09.044