Lotka-Volterra竞争扩散系统连接边界平衡点和正平衡点行波解的存在性
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摘要
本文讨论Lotka-Volterra竞争系统连接边界平衡点和正平衡点行波解的存在性。通过变量代换将边界平衡点转化为零点,再利用上下解结合不动点定理得到了当c>c*时行波解的存在性。本文的结果丰富了对Lotka-Volterra竞争系统认识。
This paper is devoted to the study of the existence of traveling wave solutions for completive Lotka-Volterra reaction-diffusion systems connectingboundary and positive equilibriums.By variable substitution boundary equilibrium can be changed into zero equilibrium.Along with upper lower solutions and Schauder's fixed point theorem we proof the existence of traveling wave solutionfor c>c*.
This paper is devoted to the study of the existence of traveling wave solutions for completive Lotka-Volterra reaction-diffusion systems connectingboundary and positive equilibriums.By variable substitution boundary equilibrium can be changed into zero equilibrium.Along with upper lower solutions and Schauder's fixed point theorem we proof the existence of traveling wave solutionfor c>c*.
引文
[1]J.D.Murray,Mathematical Biology:I.An Introduction,Springer-Verlag,New York,2002.
[2]J.D.Mathematical Biology.II Spatial Models and Biomedical Applications,Springer-Verlag,New York,2003.
[3]A.I.Volpert,V.A.Volpert,V.A.Volpert,Traveling Wave Solutions of Parabolic Systems,American Mathematical Society,Providence,Rhode Island,2000.
[4]X.Liang,X.Q.Zhao,Asymptotic speeds of spread and traveling waves for monotone semiflows with applications,Comm.Pure Appl.Math.60(1)(2007)1-40.
[5]叶其孝,李正元.反应扩散方程引论[M].北京:科学出版社,2006.
[6]W.T.Li,G.Lin,S.G.Ruan,Existence of travelling wave solutions in delayed reac-tion-diffusion systems with applications to diffusion-competition systems,Nonlin-earity 19(2006)1253-1273.
[7]K.Li,X.Li,Travelling wave solutions in diffusive and competition-cooperation systems with delays,Ima Journal of Applied Mathematics 74(4)(2009)248-291.
[8]S.A.Gourley,S.G.Ruan,Convergence and travelling fronts in functional differential equations with nonlocal terms Acompetition model,Siam J.Math.Anal.35(3)(2014)806-822.
[9]Y.Lin,Q.R.Wang,K.Zhou,Traveling wave solutions in n-dimensional delayed reaction-diffusion systems with mixed monotonicity,J.Comput.Appl.Math.243(2013)16-27.
[10]K.Zhou,Y.Lin,Q.R.Wang,Existence and asymptotics of traveling wave fronts for a delayed nonlocal diffusion model with a quiescent stage,Commun.Nonlinear Sci.Numer.Simul.18(2013)3006-3013.
[11]H.F.Weinberger,M.A.Lewis,B.T.Li,Analysis of linear determinacy for spread in cooperative models,J.Math.Biol.45,(2002)183-218.
[2]J.D.Mathematical Biology.II Spatial Models and Biomedical Applications,Springer-Verlag,New York,2003.
[3]A.I.Volpert,V.A.Volpert,V.A.Volpert,Traveling Wave Solutions of Parabolic Systems,American Mathematical Society,Providence,Rhode Island,2000.
[4]X.Liang,X.Q.Zhao,Asymptotic speeds of spread and traveling waves for monotone semiflows with applications,Comm.Pure Appl.Math.60(1)(2007)1-40.
[5]叶其孝,李正元.反应扩散方程引论[M].北京:科学出版社,2006.
[6]W.T.Li,G.Lin,S.G.Ruan,Existence of travelling wave solutions in delayed reac-tion-diffusion systems with applications to diffusion-competition systems,Nonlin-earity 19(2006)1253-1273.
[7]K.Li,X.Li,Travelling wave solutions in diffusive and competition-cooperation systems with delays,Ima Journal of Applied Mathematics 74(4)(2009)248-291.
[8]S.A.Gourley,S.G.Ruan,Convergence and travelling fronts in functional differential equations with nonlocal terms Acompetition model,Siam J.Math.Anal.35(3)(2014)806-822.
[9]Y.Lin,Q.R.Wang,K.Zhou,Traveling wave solutions in n-dimensional delayed reaction-diffusion systems with mixed monotonicity,J.Comput.Appl.Math.243(2013)16-27.
[10]K.Zhou,Y.Lin,Q.R.Wang,Existence and asymptotics of traveling wave fronts for a delayed nonlocal diffusion model with a quiescent stage,Commun.Nonlinear Sci.Numer.Simul.18(2013)3006-3013.
[11]H.F.Weinberger,M.A.Lewis,B.T.Li,Analysis of linear determinacy for spread in cooperative models,J.Math.Biol.45,(2002)183-218.