Publication: The sub-supertrajectory method. Application to the nonautonomous competition Lotka-Volterra model
Loading...
Full text at PDC
Publication Date
2010
Advisors (or tutors)
Editors
Journal Title
Journal ISSN
Volume Title
Publisher
Sociedad Española de Matemática Aplicada
Citations
Exportar
Abstract
In this paper we study in detail the pullback and forwards attractions to non-autonomous competition Lotka-Volterra system. In particular, under some conditions on the parameters, we prove the existence of a unique non-degenerate global solution for these models, which attracts any other complete bounded trajectory. For that we present the sub-supertrajectory tool as a generalization of the now classical subsupersolution method.
Description
UCM subjects
Unesco subjects
Keywords
Citation
R. S. Cantrell and C. Cosner, Practical persistence in ecological models via comparison methods, Proc. Royal Soc. Edin., 126A (1996) 247-272.
R. S. Cantrell and C. Cosner, Spatial Ecology via Reaction-Diffusion Equations, John Wiley & Sons. Ltd. 2003.
I. Chueshov, Monotone random systems theory and applications. Lecture Notes in Mathematics, 1779. Springer-Verlag, Berlin, 2002.
P. Hess, Periodic-Parabolic boundary value problems and positivity, Pitman Research Notes in Mathematics 247, Harlow Longman. 1991.
G. Hetzer, W. Shen, Uniform persistence, coexistence, and extinction in almost periodic/nonautonomous competition diffusion systems, SIAM J. Math. Anal., 34 (2002) 204-221.
J. A. Langa, J.C. Robinson, A. Rodríguez-Bernal and A. Suárez, Permanence and asymptotically stable complete trajectories for nonautonomous Lotka-Volterra models with diffusion, SIAM J. Math. Anal. 40 (2009) 2179–2216.
J. A. Langa, A. Rodríguez-Bernal and A. Suárez, On the long time behaviour of non-autonomous Lotka-Volterra models with diffusion via the sub-super trajectory method, submitted.
J. A. Langa and A. Suárez, Pullback permanence for non-autonomous partial differential equations, Electron. J. Differential Equations 2002, 72, 20 pp.
J. López-Gómez, On the structure of the permanence region for competing species models with general diffusivities and transport effects,Discrete Contin. Dyn. Syst., 2 (1996) 525-542.
C. V. Pao, Nonlinear parabolic and elliptic equations, Plenum, New York, 1992.
J.C. Robinson, A. Rodríguez-Bernal, and A. Vidal-López, Pullback attractors and extremal complete trajectories for non-autonomous reaction-diffusion problems, J. Differential Equations 238 (2007) 289–337.
A. Rodríguez-Bernal and A. Vidal-López, Existence, uniqueness and attractivity properties of positive complete trajectories for non-autonomous reaction-diffusion problems, Discrete Contin. Dyn. Syst., 18 (2007) 537–567