메뉴 건너뛰기




Volumn 195, Issue 2, 2005, Pages 524-560

Asymptotic estimates for the spatial segregation of competitive systems

Author keywords

Competing species; Monotonicity formulae; Pattern formation

Indexed keywords


EID: 18644361832     PISSN: 00018708     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.aim.2004.08.006     Document Type: Article
Times cited : (158)

References (29)
  • 1
    • 84967774571 scopus 로고
    • Variational problems with two phases and their free boundaries
    • H.W. Alt L.A. Caffarelli A. Friedman Variational problems with two phases and their free boundaries Trans. Amer. Math. Soc. 282 1984 431-461
    • (1984) Trans. Amer. Math. Soc. , vol.282 , pp. 431-461
    • Alt, H.W.1    Caffarelli, L.A.2    Friedman, A.3
  • 2
    • 80052954107 scopus 로고
    • Bifurcation of steady-state solutions in predator-prey and competition systems
    • J. Blat K.J. Brown Bifurcation of steady-state solutions in predator-prey and competition systems Proc. Roy. Soc. Edinburgh Section A 97 1984 21-34
    • (1984) Proc. Roy. Soc. Edinburgh Section A , vol.97 , pp. 21-34
    • Blat, J.1    Brown, K.J.2
  • 3
    • 0035997997 scopus 로고    scopus 로고
    • Some new monotonicity theorems with applications to free boundary problems
    • L.A. Caffarelli D. Jerison C.E. Kenig Some new monotonicity theorems with applications to free boundary problems Ann. Math. 155 2 2002 369-404
    • (2002) Ann. Math. , vol.155 , Issue.2 , pp. 369-404
    • Caffarelli, L.A.1    Jerison, D.2    Kenig, C.E.3
  • 4
    • 18644376474 scopus 로고    scopus 로고
    • Regularity for inhomogeneous two-phase free boundary problems
    • in preparation
    • L.A. Caffarelli, D. Jerison, C.E. Kenig, Regularity for inhomogeneous two-phase free boundary problems, in preparation.
    • Caffarelli, L.A.1    Jerison, D.2    Kenig, C.E.3
  • 5
    • 0034344817 scopus 로고    scopus 로고
    • Regularity of a free boundary with applications to the Pompeiu problem
    • L.A. Caffarelli L. Karp H. Shahgholian Regularity of a free boundary with applications to the Pompeiu problem Ann. Math. 151 2000 269-292
    • (2000) Ann. Math. , vol.151 , pp. 269-292
    • Caffarelli, L.A.1    Karp, L.2    Shahgholian, H.3
  • 6
    • 0037455845 scopus 로고    scopus 로고
    • An optimal partition problem related to nonlinear eigenvalues
    • M. Conti S. Terracini G. Verzini An optimal partition problem related to nonlinear eigenvalues J. Funct. Anal. 198 1 2003 160-196
    • (2003) J. Funct. Anal. , vol.198 , Issue.1 , pp. 160-196
    • Conti, M.1    Terracini, S.2    Verzini, G.3
  • 7
    • 23244445487 scopus 로고    scopus 로고
    • A variational problem for the spatial segregation of reaction-diffusion systems
    • to appear
    • M. Conti, S. Terracini, G. Verzini, A variational problem for the spatial segregation of reaction-diffusion systems, Indiana Univ. Math. J., to appear.
    • Indiana Univ. Math. J.
    • Conti, M.1    Terracini, S.2    Verzini, G.3
  • 8
    • 18644363431 scopus 로고    scopus 로고
    • On a class of optimal partition problems related to the Fučík spectrum and to the monotonicity formulae
    • to appear
    • M. Conti, S. Terracini, G. Verzini, On a class of optimal partition problems related to the Fučík spectrum and to the monotonicity formulae, Calculus Variation, to appear.
    • Calculus Variation
    • Conti, M.1    Terracini, S.2    Verzini, G.3
  • 9
    • 0021618680 scopus 로고
    • Stable coexistence in the Volterra-Lotka competition model with diffusion
    • C. Cosner A. Lazer Stable coexistence in the Volterra-Lotka competition model with diffusion SIAM J. Math. Anal. 44 1984 1112-1132
    • (1984) SIAM J. Math. Anal. , vol.44 , pp. 1112-1132
    • Cosner, C.1    Lazer, A.2
  • 10
    • 0012728860 scopus 로고
    • Competing species systems with diffusion and large interaction
    • E.N. Dancer Competing species systems with diffusion and large interaction Rend. Sem. Mat. Fis. Milano 65 1995 23-33
    • (1995) Rend. Sem. Mat. Fis. Milano , vol.65 , pp. 23-33
    • Dancer, E.N.1
  • 11
    • 0001185909 scopus 로고
    • Competing species equations with diffusion, large interactions, and jumping nonlinearities
    • E.N. Dancer Y.H. Du Competing species equations with diffusion, large interactions, and jumping nonlinearities J. Differential Equations 114 1994 434-475
    • (1994) J. Differential Equations , vol.114 , pp. 434-475
    • Dancer, E.N.1    Du, Y.H.2
  • 12
    • 58149322315 scopus 로고
    • Positive solutions for a three-species competition system with diffusion. II. The case of equal birth rates
    • E.N. Dancer Y.H. Du Positive solutions for a three-species competition system with diffusion. II. The case of equal birth rates Nonlinear Anal. 24 3 1995 359-373
    • (1995) Nonlinear Anal. , vol.24 , Issue.3 , pp. 359-373
    • Dancer, E.N.1    Du, Y.H.2
  • 13
    • 58149322315 scopus 로고
    • Positive solutions for a three-species competition system with diffusion. I. General existence results
    • E.N. Dancer Y.H. Du Positive solutions for a three-species competition system with diffusion. I. General existence results Nonlinear Anal. 24 3 1995 359-373
    • (1995) Nonlinear Anal. , vol.24 , Issue.3 , pp. 359-373
    • Dancer, E.N.1    Du, Y.H.2
  • 14
    • 0037650204 scopus 로고    scopus 로고
    • On a free boundary problem arising from population biology
    • E.N. Dancer Y.H. Du On a free boundary problem arising from population biology Indiana Univ. Math. J. 52 1 2003 51-67
    • (2003) Indiana Univ. Math. J. , vol.52 , Issue.1 , pp. 51-67
    • Dancer, E.N.1    Du, Y.H.2
  • 15
    • 0001853554 scopus 로고
    • Uniqueness and stability for solutions of competing species equations with large interactions
    • E.N. Dancer Z.M. Guo Uniqueness and stability for solutions of competing species equations with large interactions Comm. Appl. Nonlinear Anal. 1 1994 19-45
    • (1994) Comm. Appl. Nonlinear Anal. , vol.1 , pp. 19-45
    • Dancer, E.N.1    Guo, Z.M.2
  • 17
    • 0028517768 scopus 로고
    • Dynamics of interfaces in competition-diffusion systems
    • S-I. Ei E. Yanagida Dynamics of interfaces in competition-diffusion systems SIAM J. Appl. Math. 54 5 1994 1355-1373
    • (1994) SIAM J. Appl. Math. , vol.54 , Issue.5 , pp. 1355-1373
    • Ei, S.-I.1    Yanagida, E.2
  • 19
    • 84990585735 scopus 로고
    • Uniqueness and nonuniqueness of coexistence states in the Lotka-Volterra competition model
    • C. Gui Y. Lou Uniqueness and nonuniqueness of coexistence states in the Lotka-Volterra competition model Comm. Pure Appl. Math. 47 12 1994 1571-1594
    • (1994) Comm. Pure Appl. Math. , vol.47 , Issue.12 , pp. 1571-1594
    • Gui, C.1    Lou, Y.2
  • 20
    • 0000716962 scopus 로고
    • On the existence and uniqueness of positive steady states in Lotka-Volterra ecological models with diffusion
    • P. Korman A. Leung On the existence and uniqueness of positive steady states in Lotka-Volterra ecological models with diffusion Appl. Anal. 26 1987 145-160
    • (1987) Appl. Anal. , vol.26 , pp. 145-160
    • Korman, P.1    Leung, A.2
  • 21
    • 0001509567 scopus 로고
    • On steady state solutions of a system of reaction-diffusion equations from biology
    • A.C. Lazer P.J. McKenna On steady state solutions of a system of reaction-diffusion equations from biology Nonlinear Anal. TMA 6 1982 523-530
    • (1982) Nonlinear Anal. TMA , vol.6 , pp. 523-530
    • Lazer, A.C.1    McKenna, P.J.2
  • 22
    • 0347055376 scopus 로고    scopus 로고
    • On 3 × 3 Lotka-Volterra competition systems with cross-diffusion
    • Y. Lou S. Martínez W.-M. Ni On 3 × 3 Lotka-Volterra competition systems with cross-diffusion Discrete Continuous Dynamics Systems 6 1 2000 175-190
    • (2000) Discrete Continuous Dynamics Systems , vol.6 , Issue.1 , pp. 175-190
    • Lou, Y.1    Martínez, S.2    Ni, W.-M.3
  • 23
    • 0030579038 scopus 로고    scopus 로고
    • Diffusion self-diffusion and cross-diffusion
    • Diffusion Y. Lou W.-M. Ni self-diffusion and cross-diffusion J. Differential Equations 131 1 1996 79-131
    • (1996) J. Differential Equations , vol.131 , Issue.1 , pp. 79-131
    • Lou, Y.1    Ni, W.-M.2
  • 24
    • 84998211051 scopus 로고
    • Pattern formation in competition-diffusion systems in nonconvex domains
    • H. Matano M. Mimura Pattern formation in competition-diffusion systems in nonconvex domains Publ. Res. Inst. Math. Sci. 19 3 1983 1049-1079
    • (1983) Publ. Res. Inst. Math. Sci. , vol.19 , Issue.3 , pp. 1049-1079
    • Matano, H.1    Mimura, M.2
  • 25
    • 0347856582 scopus 로고
    • Spatial distribution of competing species
    • Mathematical Ecology (Trieste, 1982)
    • M. Mimura, Masayasu, Spatial distribution of competing species, Mathematical Ecology (Trieste, 1982), Lecture Notes in Biomathematics, vol. 54, 1982, pp. 492-501.
    • (1982) Lecture Notes in Biomathematics , vol.54 , pp. 492-501
    • Mimura, M.1    Masayasu2
  • 26
    • 0021744971 scopus 로고
    • The effects of interference competition on stability, structure and invasion of a multispecies system
    • N. Shigesada K. Kawasaki E. Teramoto The effects of interference competition on stability, structure and invasion of a multispecies system J. Math. Biol. 21 2 1984 97-113
    • (1984) J. Math. Biol. , vol.21 , Issue.2 , pp. 97-113
    • Shigesada, N.1    Kawasaki, K.2    Teramoto, E.3
  • 27
    • 0000866786 scopus 로고
    • Zur symmetrisierung von funktionen auf spharen
    • E. Sperner Zur symmetrisierung von funktionen auf spharen Math. Z 134 1973 317-330
    • (1973) Math. Z. , vol.134 , pp. 317-330
    • Sperner, E.1
  • 28
    • 0004475031 scopus 로고    scopus 로고
    • On the regularity of a chemical reaction interface
    • Y. Tonegawa On the regularity of a chemical reaction interface Comm. Partial Differential Equations 23 7-8 1998 1181-1207
    • (1998) Comm. Partial Differential Equations , vol.23 , Issue.7-8 , pp. 1181-1207
    • Tonegawa, Y.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.