Some new results in competing systems with many species
Wang, Kelei ; Zhang, Zhitao
Annales de l'I.H.P. Analyse non linéaire, Tome 27 (2010), p. 739-761 / Harvested from Numdam
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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.

Publié le : 2010-01-01
DOI : https://doi.org/10.1016/j.anihpc.2009.11.004
Classification:  35B40,  35R35,  92D25,  35K57,  58E20 
@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},
     volume = {27},
     year = {2010},
     pages = {739-761},
     doi = {10.1016/j.anihpc.2009.11.004},
     mrnumber = {2595199},
     zbl = {1201.35113},
     language = {en},
     url = {http://dml.mathdoc.fr/item/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) pp. 739-761. doi : 10.1016/j.anihpc.2009.11.004. http://gdmltest.u-ga.fr/item/AIHPC_2010__27_2_739_0/

[1] L.A. Caffarelli, A.L. Karakhanyan, F. Lin, The geometry of solutions to a segregation problem for non-divergence systems, J. Fixed Point Theory Appl. 5 no. 2 (2009), 319-351 | MR 2529504 | Zbl 1217.35015

[2] L.A. Caffarelli, F. Lin, An optimal partition problem for eigenvalues, J. Sci. Comput. 31 no. 1 (2007), 5-18 | MR 2304268 | Zbl 1123.65060

[3] L.A. Caffarelli, F. Lin, Singularly perturbed elliptic systems and multi-valued harmonic functions with free boundaries, J. Amer. Math. Soc. 21 (2008), 847-862 | MR 2393430 | Zbl 1194.35138

[4] L.A. Caffarelli, F. Lin, Nonlocal heat flows preserving the L2 energy, Discrete Contin. Dyn. Syst. 23 no. 1/2 (2009), 49-64 | MR 2449068 | Zbl 1154.35364

[5] M. Conti, S. Terracini, G. Verzini, A variational problem for the spatial segregation of reaction diffusion systems, Indiana Univ. Math. J. 54 no. 3 (2005), 779-815 | MR 2151234 | Zbl 1132.35397

[6] M. Conti, S. Terracini, G. Verzini, Asymptotic estimates for the spatial segregation of competitive systems, Adv. Math. 195 no. 2 (2005), 524-560 | MR 2146353 | Zbl 1126.35016

[7] M. Conti, S. Terracini, G. Verzini, Uniqueness and least energy property for strongly competing systems, Interfaces Free Bound. 8 (2006), 437-446 | MR 2283921 | Zbl 1103.92041

[8] E.N. Dancer, Yihong Du, Positive solutions for a three-species competition system with diffusion, I. General existence results, Nonlinear Anal. 24 no. 3 (1995), 337-357 | MR 1312772 | Zbl 0824.35033

[9] E.N. Dancer, Yihong Du, 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 1312773 | Zbl 0824.35034

[10] E.N. Dancer, Zhitao Zhang, Dynamics of Lotka–Volterra competition systems with large interaction, J. Differential Equations 182 no. 2 (2002), 470-489 | MR 1900331 | Zbl 1006.35047

[11] M. Gromov, R. Schoen, 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 | Numdam | Zbl 0896.58024

[12] Qing Han, F. Lin, Nodal Sets of Solutions of Elliptic Differential Equations, books available on Han's homepage

[13] Anthony W. Leung, Systems of Nonlinear Partial Differential Equations: Applications to Biology and Engineering, Kluwer Academic Publishers, Dordrecht (1989) | MR 1621827 | Zbl 0691.35002

[14] F. Lin, X. Yang, Geometric measure theory an introduction, Advanced Mathematics, Beijing/Boston, 1, Science Press/International Press, Beijing/Boston (2002) | MR 2030862 | Zbl 1074.49011

[15] S. Smale, On the differential equations of species in competition, J. Math. Biol. 3 (1976), 5-7 | MR 406579 | Zbl 0344.92009