In this paper, we prove some uniqueness and convergence results for a competing system and its singular limit, and an interior measure estimate of the free boundary for the singular limit.
Mots clés : Competing species, Free boundary problem, Harmonic map into singular space
@article{AIHPC_2010__27_2_739_0, author = {Wang, Kelei and Zhang, Zhitao}, title = {Some new results in competing systems with many species}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {739--761}, publisher = {Elsevier}, volume = {27}, number = {2}, year = {2010}, doi = {10.1016/j.anihpc.2009.11.004}, mrnumber = {2595199}, zbl = {1201.35113}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.anihpc.2009.11.004/} }
TY - JOUR AU - Wang, Kelei AU - Zhang, Zhitao TI - Some new results in competing systems with many species JO - Annales de l'I.H.P. Analyse non linéaire PY - 2010 SP - 739 EP - 761 VL - 27 IS - 2 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.anihpc.2009.11.004/ DO - 10.1016/j.anihpc.2009.11.004 LA - en ID - AIHPC_2010__27_2_739_0 ER -
%0 Journal Article %A Wang, Kelei %A Zhang, Zhitao %T Some new results in competing systems with many species %J Annales de l'I.H.P. Analyse non linéaire %D 2010 %P 739-761 %V 27 %N 2 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.anihpc.2009.11.004/ %R 10.1016/j.anihpc.2009.11.004 %G en %F AIHPC_2010__27_2_739_0
Wang, Kelei; Zhang, Zhitao. Some new results in competing systems with many species. Annales de l'I.H.P. Analyse non linéaire, Tome 27 (2010) no. 2, pp. 739-761. doi : 10.1016/j.anihpc.2009.11.004. http://archive.numdam.org/articles/10.1016/j.anihpc.2009.11.004/
[1] The geometry of solutions to a segregation problem for non-divergence systems, J. Fixed Point Theory Appl. 5 no. 2 (2009), 319-351 | MR | Zbl
, , ,[2] An optimal partition problem for eigenvalues, J. Sci. Comput. 31 no. 1 (2007), 5-18 | MR | Zbl
, ,[3] Singularly perturbed elliptic systems and multi-valued harmonic functions with free boundaries, J. Amer. Math. Soc. 21 (2008), 847-862 | MR | Zbl
, ,[4] Nonlocal heat flows preserving the L2 energy, Discrete Contin. Dyn. Syst. 23 no. 1/2 (2009), 49-64 | MR | Zbl
, ,[5] A variational problem for the spatial segregation of reaction diffusion systems, Indiana Univ. Math. J. 54 no. 3 (2005), 779-815 | MR | Zbl
, , ,[6] Asymptotic estimates for the spatial segregation of competitive systems, Adv. Math. 195 no. 2 (2005), 524-560 | MR | Zbl
, , ,[7] Uniqueness and least energy property for strongly competing systems, Interfaces Free Bound. 8 (2006), 437-446 | MR | Zbl
, , ,[8] Positive solutions for a three-species competition system with diffusion, I. General existence results, Nonlinear Anal. 24 no. 3 (1995), 337-357 | MR | Zbl
, ,[9] Positive solutions for a three-species competition system with diffusion, II: The case of equal birth rates, Nonlinear Anal. 24 no. 3 (1995), 359-373 | MR | Zbl
, ,[10] Dynamics of Lotka–Volterra competition systems with large interaction, J. Differential Equations 182 no. 2 (2002), 470-489 | MR | Zbl
, ,[11] Harmonic maps into singular spaces and p-adic superrigidity for lattices in groups of rank one, Publ. Math. Inst. Hautes Etudes Sci. 76 no. 1 (1992), 165-246 | EuDML | Numdam | Zbl
, ,[12] Qing Han, F. Lin, Nodal Sets of Solutions of Elliptic Differential Equations, books available on Han's homepage
[13] Systems of Nonlinear Partial Differential Equations: Applications to Biology and Engineering, Kluwer Academic Publishers, Dordrecht (1989) | MR | Zbl
,[14] Geometric measure theory an introduction, Advanced Mathematics, Beijing/Boston, 1, Science Press/International Press, Beijing/Boston (2002) | MR | Zbl
, ,[15] On the differential equations of species in competition, J. Math. Biol. 3 (1976), 5-7 | MR | Zbl
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