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研究生:陳韻儀
研究生(外文):Yun-Yi Chen
論文名稱:三種競爭合作系統之行波解的存在性
論文名稱(外文):Existence of traveling waves solutions for a three species competition-cooperation system
指導教授:許正雄許正雄引用關係
指導教授(外文):Cheng-Hsiung Hsu
學位類別:碩士
校院名稱:國立中央大學
系所名稱:數學系
學門:數學及統計學門
學類:數學學類
論文出版年:2018
畢業學年度:106
語文別:中文
論文頁數:35
中文關鍵詞:物種競爭模型存在性行波解
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本文研究了具有一般非線性的三種競爭合作系統之行波解的存在性。該模型可以從空間平均和時間延遲的Lotka-Volterra系統中推導出來。首先,我們引用KPP方程和兩種Lotka-Volterra競爭系統的行波解的一些性質。接著,使用這個行波解,我們可以為我們的模型建構一對上下解。藉由單調迭代法,我們可以導出行波解的存在性。此外,我們舉例說明一些例子來支持我們的結果。事實上,我們稍微將[5]的結果擴展到更一般的非線性。
In this thesis, we study the existence of traveling wave solutions for a three species competition cooperation system with general nonlinearity. The model can be derived from a spatially averaged and temporally delayed Lotka-Volterra system. First, we recall some properties of traveling wave solutions for KPP equation and two species Lotka-Volterra competition system. Using these traveling wave solutions, we can construct a pair of upper and lower solutions for our model. Then, by using the technique of monotone iteration method, we can derive the existence of the traveling wave solutions. Furthermore, we illustrate some examples to support our result. In fact, we minor extend the results of [5] to more general nonlinearity.
摘要 ……………………………………………………………… i
ABSTRACT ……………………………………………………………… ii
目錄 ……………………………………………………………… iii
1 Introduction……………………………………………… 1
2 Some known results……………………………………… 4
3 Construction of upper and lower solutions……… 6
  3.1 (A1) and (A2a) hold…………………………………… 6
  3.2 (A1), (A2b) and (A3) hold…………………………… 9
4 Main theorem…………………………… 19
5 Examples…………………………………………………… 24
References ……………………………………………………………… 27
[1] P.Ashwin,M.V.Bartuccelli,T.J.BridgesandS.A.Gourley,Travellingfrontsforthe
KPP equationwithspatio-temporaldelay, Zeitschrift furAngewandteMathematikund
Physik , 53(2002),103-122.
[2] H. BerestyckiandL.Nirenberg,SomeQualitativePropertiesofSolutionsofSemilinear
Elliptic EquationsinCylindricalDomains, J. GeometryandPhys.,ed.byP.Rabinowitz,
AcademicPress, 1990,115-164.
[3] A. BoumenirandV.Nguyen,Perrontheoreminmonotoneiterationmethodfortraveling
wavesindelayedreaction-diusionequations, J. Di.Eqs., 244(2008),1551-1570.
[4] N. FeiandJ.Carr,Existenceoftravellingwaveswiththeirminimalspeedforadiusing
Lotka-Volterrasystem, NonlinearAnalysis:RealWorldApplications, 4(2003),503-524.
[5] X.Hou andY.Li,Travelingwavesinathreespeciescompetition-cooperationsystem,
Comunicationsonpureandappliedanalysis, 4(2017),1103-1119.
[6] Y. Hosono,TravellingwavesforadiusiveLotka-VolterracompetitionmodelI:Singular
Perturbations, DiscreteandContinuousDynamicalSystems-SeriesB, 3(2003),79-95.
[7] W. Huang,ProblemonminimumwavespeedforaLotka-Volterrareaction-diusion
competitionmodel, J. Dynam.DierentialEquations, 22(2010),285-297.
[8] J. I.Kanel,Onthewavefrontofacompetition-diusionsysteminpopalationdynamics,
Nonlinear Analysis,65(2006),301-320.
[9] J. I.KanelandL.Zhou,Existenceofwavefrontsolutionsandestimatesofwavespeedfor
a competition-diusionsystem, NonlinearAnalysis,Theory,MethodsandApplications,
27 (1996),579-587.
[10] Y. Kan-on,Noteonpropagationspeedoftravellingwavesforaweaklycoupledparabolic
system, NonlinearAnalysis, 44(2001),239-246.
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NonlinearAnalysis,Theory,methodsandApplications, 28(1997),145-164.
[12] A. W.Leung,X.HouandW.Feng,TravelingwavesolutionsforLotka-Volterrasystem
revisited, DiscreteandContinuousDynamicalSystems-SeriesB, 15(2011),171-196.
[13] D. Sattinger,Onthestabilityoftravelingwaves, Adv.inMath., 22(1976),312-355.
[14] I. Volpert,V.VolpertandV.Volpert, TravelingWaveSolutionsofParabolicSystems,
Transl.Math.Monogr.,vol140,Amer.Math.Soc.,Providence,RI.1994.
[15] J. WuandX.Zou,Travelingwavefrontsofreaction-diusionsystemswithdelay, J.
Dynamics andDi.Eq., 13(2001),651-687.andErratumtotravelingwavefrontsof
reaction-diusion systemswithdelay, J. DynamicsandDi.Eq., 2(2008),531-533.
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