一类具时间周期和非局部时滞的非拟单调反应扩散方程的整体解

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一类具时间周期和非局部时滞的非拟单调反应扩散方程的整体解王双明兰州财经大学信息工程学院, 兰州 730020 Reaction-diffusion Equation without Quasi-monotonicity WANG ShuangmingSchool of Information Engineering, Lanzhou University of Finance and Economics, Lanzhou 730020, China

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摘要研究了一类不具有拟单调性的时间周期非局部时滞反应扩散方程的新型整体解.为了克服拟单调性条件缺失带来的困难，借助于两个拟单调辅助方程的周期行波解和相应空间齐次方程的全轨道构造了新型的整体解.

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收稿日期: 2019-06-28

PACS:

O175

基金资助:甘肃省科技计划（18JR3RA217），甘肃省高等学校创新基金项目（2020A-062），兰州财经大学科研项目（Lzufe2019B-006）资助.

引用本文:

王双明. 一类具时间周期和非局部时滞的非拟单调反应扩散方程的整体解[J]. 应用数学学报, 2020, 43(4): 668-683. WANG Shuangming. Reaction-diffusion Equation without Quasi-monotonicity. Acta Mathematicae Applicatae Sinica, 2020, 43(4): 668-683.

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[1]	Jin Y, Zhao X Q. Spatial dynamics of a non-local periodic reaction-diffusion model with stage structure. SIAM J. Math. Anal., 2009, 40(6):2496-2516
[2]	Zhang L, Wang Z C, Zhao X Q. Propagation dynamics of a time periodic and delayed reaction-diffusion model without quasi-monotonicity. Trans. Amer. Math. Soc., 2019, 372(3):1751-1782
[3]	Li P, Wu S L. Monostable traveling waves for a time-periodic and delayed nonlocal reaction-diffusion equation. Z. Angew. Math. Phys., 2018, 69(2)39:1-16, http://doi.org/10.1007/s00033-018-0936-7
[4]	Hamel F, Nadirashvili N. Entire solutions of the KPP equation. Commun. Pure Appl. Math., 1999, 52(10):1255-1276
[5]	Hamel F, Nadirashvili N. Travelling fronts and entire solutions of the Fisher-KPP equation in RN. Arch. Ration. Mech. Analysis, 2001, 157(2):91-163
[6]	Chen X F, Guo J S. Existence and uniqueness of entire solutions for a reaction-diffusion equation. J. Differential Equations., 2005, 212(1):62-84
[7]	Chen X F, Guo J S, Ninomiya H. Entire solutions of reaction-diffusion equations with balanced bistable nonlinearities. Proc. Roy. Soc. Edinburgh Sect. A, 2006, 136(06):1207-1237
[8]	Morita Y, Ninomiya H. Entire solutions with merging fronts to reaction-diffusion equations. J. Dynam. Diff. Eqns., 2006, 18(4):841-861
[9]	Chen Y Y, Guo J S, Ninomiya H, Yao C H. Entire solutions originating from monotone fronts to the Allen-Cahn equation. Phys. D, 2018, 378/379:1-19
[10]	Wang Z C, Li W T, Wu J H. Entire solutions in delayed lattice differential equations with monostable nonlinearity. SIAM J. Math. Anal., 2009, 40(6):2392-2420
[11]	Fukao Y, Morita Y, Ninomiya H. Some entire solutions of the Allen-Cahn equation. Taiwan. J. Math. 2004, 8(1):15-32
[12]	Guo J S, Morita Y. Entire solutions of reaction-diffusion equations and an application to discrete diffusive equations. Discrete Contin. Dynam. Syst., 2005, 12(2):193-212
[13]	Yagisita H. Backward global solutions characterizing annihilation dynamics of traveling fronts. Publ. Res. Inst. Math. Sci., 2003, 39(1):117-164
[14]	Li W T, Liu N W, Wang Z C. Entire solutions in reaction-advection-diffusion equations in cylinders. J. Math. Pures Appl., 2008, 90(5):492-504
[15]	Li W T, Wang Z C, Wu J H. Entire solutions of monostable reaction-diffusion equations with delayed nonlinearity. J. Differential Equations, 2008, 245(1):102-129
[16]	Wang Z C, Li W T. Dynamics of a non-local delayed reaction-diffusion equation without quasi-monotonicity. Proc. Roy. Soc. Edinburgh Sect. A, 2010, 140(05):1081-1109
[17]	Wang Z C, Li W T, Ruan S G. Entire solutions in bistable reaction-diffusion equations with nonlocal delayed nonlinearity. Trans. Amer. Math. Soc., 2008, 361(4):2047-2084
[18]	Wu S L, Hsu C H. Entire solutions of nonlinear cellular neural networks with distributed time delays. Nonlinearity, 2012, 25(9):2785-2801
[19]	Wu S L, Hsu C H. Entire solutions of non-quasi-monotone delayed reaction-diffusion equations with applications. Proc. Roy. Soc. Edinburgh Sect. A, 2014, 144(5):1085-1112
[20]	Wu S L, Ruan S G. Entire solutions for nonlocal dispersal equations with spatio-temporal delay:monostable case. J. Differential Equations, 2015, 258(7):2435-2470
[21]	Ma S W. Traveling waves for non-local delayed diffusion equations via auxiliary equation. J. Differential Equations, 2007, 237(2):259-277
[22]	Sheng W J, Cao M L. Entire solutions of the Fisher-KPP equation in time periodic media. Dyn. Partial Differ. Equ., 2012, 9(2):133-145
[23]	Sheng W J, Wang J B. Entire solutions of time periodic bistable reaction-advection-diffusion equations in infinite cylinders. J. Math. Phy., 2015, 56(8):2777-2805
[24]	Wang Z C, Zhang L, Zhao X Q. Time periodic traveling waves for a periodic and diffusive SIR epidemic model. J. Dynam. Differential Equations, 2018, 30(1):379-403
[25]	Daners D, Koch-Medina P. Abstract Evolution Equations, Periodic Problems and Applications, Pitman Research Notes in Mathematics Series, 279. Longman:Harlow, UK, 1992
[26]	Smith H L. Monotonic Dynamical Systems:An Introduction to the Theory of Competitive and Cooperative systems. Mathematical Surveys and Monographs, American Mathematical Society:Providence, 41, 1995
[27]	Xu D S, Zhao X Q. Dynamics in a periodic competitive model with stage structure. J. Math. Anal. Appl., 2005, 311(2):417-438
[28]	Zhao X Q. Dynamical Systems in Population Biology. New York:Springer-Verlag, 2017

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