메뉴 건너뛰기




Volumn 51, Issue 1, 2005, Pages 75-113

Analysis of the periodically fragmented environment model: I - Species persistence

Author keywords

[No Author keywords available]

Indexed keywords


EID: 22244440170     PISSN: 03036812     EISSN: 14321416     Source Type: Journal    
DOI: 10.1007/s00285-004-0313-3     Document Type: Review
Times cited : (270)

References (51)
  • 1
    • 32744464143 scopus 로고
    • Differential equations (Birmingham, Ala., 1983)
    • Agmon, S.: Differential equations (Birmingham, Ala., 1983). North-Holland Math. Stud. 92, 7-17 (1984)
    • (1984) North-Holland Math. Stud. , vol.92 , pp. 7-17
    • Agmon, S.1
  • 2
    • 84989773336 scopus 로고    scopus 로고
    • Ammerman, A.J., Cavalli-Sforza, L.L.: The Neolithic Transition and the Genetics of Populations in Europe. Princeton Univ. Press, Princeton, NJ, 1984
  • 3
    • 49349119963 scopus 로고
    • Multidimensional nonlinear diffusions arising in population genetics
    • Aronson, D.G., Weinberger, H.F.: Multidimensional nonlinear diffusions arising in population genetics. Adv. Math. 30, 33-76 (1978)
    • (1978) Adv. Math. , vol.30 , pp. 33-76
    • Aronson, D.G.1    Weinberger, H.F.2
  • 4
    • 0001808883 scopus 로고
    • Le nombre de solutions de certains problèmes semi-linéaires elliptiques
    • Berestycki, H.: Le nombre de solutions de certains problèmes semi-linéaires elliptiques. J. Func. Anal. 40, 1-29 (1981)
    • (1981) J. Func. Anal. , vol.40 , pp. 1-29
    • Berestycki, H.1
  • 5
    • 0036298883 scopus 로고    scopus 로고
    • Front propagation in periodic excitable media
    • Berestycki, H., Hamel, F.: Front propagation in periodic excitable media. Commun. Pure Appl. Math. 55, 949-1032 (2002)
    • (2002) Commun. Pure Appl. Math. , vol.55 , pp. 949-1032
    • Berestycki, H.1    Hamel, F.2
  • 6
    • 16644384785 scopus 로고    scopus 로고
    • The speed of propagation for KPP type problems. I - Periodic framework
    • J. Europ. Math. Soc. 2005
    • Berestycki, H., Hamel, F., Nadirashvili, N.: The speed of propagation for KPP type problems. I - Periodic framework. J. Europ. Math. Soc. 2005. J. Eur. Math. Soc. 7, 173-213 (2005)
    • (2005) J. Eur. Math. Soc. , vol.7 , pp. 173-213
    • Berestycki, H.1    Hamel, F.2    Nadirashvili, N.3
  • 7
    • 16644386250 scopus 로고    scopus 로고
    • Berestycki, H., Hamel, F., Roques, L.: Analysis of the periodically fragmented environment model : II - Biological invasions and pulsating travelling fronts. J. Math. Pures Appl. 2005. To appear
  • 8
    • 34247526880 scopus 로고    scopus 로고
    • Liouville-type results for semilinear elliptic equations in unbounded domains
    • Annali di Matematica Pura ed Applicata
    • Berestycki, H., Hamel, F., Rossi, L.: Liouville-type results for semilinear elliptic equations in unbounded domains ,Annali di Matematica Pura ed Applicata,186,3,469-507
    • (2007) Annali di Matematica Pura ed Applicata , vol.186 , Issue.3 , pp. 469-507
    • Berestycki, H.1    Hamel, F.2    Rossi, L.3
  • 9
    • 4644290043 scopus 로고    scopus 로고
    • Some properties of monotone rearrangement with applications to elliptic equations in cylinders
    • Berestycki, H., Lachand-Robert, T.: Some properties of monotone rearrangement with applications to elliptic equations in cylinders. Math. Nachr. 266, 3-19 (2004)
    • (2004) Math. Nachr. , vol.266 , pp. 3-19
    • Berestycki, H.1    Lachand-Robert, T.2
  • 11
    • 84990602584 scopus 로고
    • The principal eigenvalue and maximum principle for second order elliptic operators in general domains
    • Berestycki, H., Nirenberg, L., Varadhan, S.R.S.: The principal eigenvalue and maximum principle for second order elliptic operators in general domains. Commun. Pure Appl. Math. 47, 47-92 (1994)
    • (1994) Commun. Pure Appl. Math. , vol.47 , pp. 47-92
    • Berestycki, H.1    Nirenberg, L.2    Varadhan, S.R.S.3
  • 12
    • 0000441550 scopus 로고
    • On the existence of positive eigenfunctions for an eigenvalue problem with indefinite weight function
    • Brown, K., Lin, S.S.: On the existence of positive eigenfunctions for an eigenvalue problem with indefinite weight function. J. Math. Anal. Appl. 75, 112-120 (1980)
    • (1980) J. Math. Anal. Appl. , vol.75 , pp. 112-120
    • Brown, K.1    Lin, S.S.2
  • 13
    • 0000883114 scopus 로고
    • Diffusive logistic equations with indefinite weights: Population models in disrupted environments
    • Cantrell, R.S., Cosner, C.: Diffusive logistic equations with indefinite weights: population models in disrupted environments. Proc. Roy. Soc. Edinburgh 112, 293-318 (1989)
    • (1989) Proc. Roy. Soc. Edinburgh , vol.112 , pp. 293-318
    • Cantrell, R.S.1    Cosner, C.2
  • 14
    • 0000426851 scopus 로고
    • Diffusive logistic equations with indefinite weights: Population models in disrupted environments II
    • Cantrell, R.S., Cosner, C.: Diffusive logistic equations with indefinite weights: population models in disrupted environments II. SIAM J. Math. Anal. 22 (4), 1043-1064 (1991)
    • (1991) SIAM J. Math. Anal. , vol.22 , Issue.4 , pp. 1043-1064
    • Cantrell, R.S.1    Cosner, C.2
  • 15
    • 0000371382 scopus 로고
    • The effects of spatial heterogeneity in population dynamics
    • Cantrell, R.S., Cosner, C.: The effects of spatial heterogeneity in population dynamics. J. Math. Biol. 29, 315-338 (1991)
    • (1991) J. Math. Biol. , vol.29 , pp. 315-338
    • Cantrell, R.S.1    Cosner, C.2
  • 16
    • 0004487623 scopus 로고    scopus 로고
    • On the effects of spatial heterogeneity on the persistence of interacting species
    • Cantrell, R.S., Cosner, C.: On the effects of spatial heterogeneity on the persistence of interacting species. J. Math. Biol. 37, 103-145 (1998)
    • (1998) J. Math. Biol. , vol.37 , pp. 103-145
    • Cantrell, R.S.1    Cosner, C.2
  • 17
    • 0036339156 scopus 로고    scopus 로고
    • Homogenization of a neutronic critical diffusion problem with drift
    • Capdeboscq, Y.: Homogenization of a neutronic critical diffusion problem with drift. Proc. Royal Soc. Edinburgh 132 A, 567-594 (2002)
    • (2002) Proc. Royal Soc. Edinburgh , vol.132 A , pp. 567-594
    • Capdeboscq, Y.1
  • 19
    • 84989780408 scopus 로고    scopus 로고
    • Cavalli-Sforza, L.L., Feldman, M.W.: Cultural Transmission and Evolution : A Quantitative Approach. Princeton Univ. Press, Princeton, NJ, 1981
  • 20
    • 17144459686 scopus 로고    scopus 로고
    • Local extinction versus local exponential growth for spatial branching processes
    • Engländer, J., Kyprianou, A.E.: Local extinction versus local exponential growth for spatial branching processes. Ann. Probab. 32, 78-99 (2004)
    • (2004) Ann. Probab. , vol.32 , pp. 78-99
    • Engländer, J.1    Kyprianou, A.E.2
  • 23
    • 0017637590 scopus 로고
    • The approach of solutions of non-linear diffusion equations to traveling front solutions
    • Fife, P.C., McLeod, J.B.: The approach of solutions of non-linear diffusion equations to traveling front solutions. Arch. Ration. Mech. Anal. 65, 335-361 (1977)
    • (1977) Arch. Ration. Mech. Anal. , vol.65 , pp. 335-361
    • Fife, P.C.1    McLeod, J.B.2
  • 24
    • 0000268135 scopus 로고
    • The advance of advantageous genes
    • Fisher, R.A.: The advance of advantageous genes. Ann. Eugenics 7, 335-369 (1937)
    • (1937) Ann. Eugenics , vol.7 , pp. 335-369
    • Fisher, R.A.1
  • 25
    • 4043166736 scopus 로고
    • On wavefront propagation in periodic media. Stochastic analysis and applications
    • Dekker, New York
    • Freidlin, M.: On wavefront propagation in periodic media. Stochastic analysis and applications, Adv. Probab. (Related Topics, 7, Dekker, New York, 1984) 147-166
    • (1984) Adv. Probab. (Related Topics) , vol.7 , pp. 147-166
    • Freidlin, M.1
  • 26
    • 0040185425 scopus 로고
    • Semi-linear PDEs and limit theorem for large deviations
    • Freidlin, M.: Semi-linear PDEs and limit theorem for large deviations. Springer Lecture Notes in Mathematics, 1527, 1992
    • (1992) Springer Lecture Notes in Mathematics , vol.1527
    • Freidlin, M.1
  • 27
    • 84989786844 scopus 로고    scopus 로고
    • Freidlin, M.: Markov Processes and Differential Equations: Asymptotic Problems. Lectures in Mathematics ETH Zurich, Birkhauser Verlag, Basel, 1996
  • 28
    • 0008835676 scopus 로고
    • On the propagation of concentration waves in periodic and random media
    • Gärtner, J., Freidlin, M.: On the propagation of concentration waves in periodic and random media. Sov. Math. Dokl. 20, 1282-1286 (1979)
    • (1979) Sov. Math. Dokl. , vol.20 , pp. 1282-1286
    • Gärtner, J.1    Freidlin, M.2
  • 29
    • 84989766259 scopus 로고    scopus 로고
    • Hardy, G.H., Littlewood, J.E., P'olya, G.: Inequalities. Cambridge University Press, Cambridge, 1952
  • 30
    • 0035527623 scopus 로고    scopus 로고
    • On the placement of an obstacle or a well so as to optimize the fundamental eigenvalue
    • Harrell, E.M., Kröger, P., Kurata, K.: On the placement of an obstacle or a well so as to optimize the fundamental eigenvalue. SIAM J. Math. Anal. 33 (1), 240-259 (2001)
    • (2001) SIAM J. Math. Anal. , vol.33 , Issue.1 , pp. 240-259
    • Harrell, E.M.1    Kröger, P.2    Kurata, K.3
  • 31
    • 0003323485 scopus 로고
    • Periodic-parabolic boundary value problems and positivity
    • Longman Scientific & Technical, Harlow, UK
    • Hess, P.: Periodic-parabolic boundary value problems and positivity. Pitman Research Notes in Mathematics Series, 247. Longman Scientific & Technical, Harlow, UK, 1991
    • (1991) Pitman Research Notes in Mathematics Series , vol.247
    • Hess, P.1
  • 32
    • 0033923261 scopus 로고    scopus 로고
    • Populations on Fragmented Landscapes with Spatially Structured Heterogeneities: Landscape Generation and Local Dispersal
    • Hiebeler, D.E.: Populations on Fragmented Landscapes with Spatially Structured Heterogeneities: Landscape Generation and Local Dispersal. Ecology 81 (6), 1629-1641 (2000)
    • (2000) Ecology , vol.81 , Issue.6 , pp. 1629-1641
    • Hiebeler, D.E.1
  • 33
    • 0141970998 scopus 로고
    • Existence of travelling waves for reaction-diffusion equations of Fisher type in periodic media
    • Equations. J. Henderson (ed.), World Scientific
    • Hudson, W., Zinner, B.: Existence of travelling waves for reaction-diffusion equations of Fisher type in periodic media. In: Boundary Value Problems for Functional-Differential Equations. J. Henderson (ed.), World Scientific, 1995, pp. 187-199
    • (1995) Boundary Value Problems for Functional-Differential , pp. 187-199
    • Hudson, W.1    Zinner, B.2
  • 34
    • 84989768530 scopus 로고    scopus 로고
    • Hughes, J.: Modeling the effect of landscape pattern on mountain pine beetles. Thesis, Simon Fraser University, 2002
  • 35
    • 0035747963 scopus 로고    scopus 로고
    • The Evolution of dispersal rates in a heterogeneous time-periodic environment
    • Hutson, V., Mischaikow, K., Polacik, P.: The Evolution of dispersal rates in a heterogeneous time-periodic environment. J. Math. Biol. 43, 501-533 (2001)
    • (2001) J. Math. Biol. , vol.43 , pp. 501-533
    • Hutson, V.1    Mischaikow, K.2    Polacik, P.3
  • 36
    • 32744474606 scopus 로고
    • Simulations of the heterogeneity of environments by finite element methods
    • Kaipio, J.P., Tervo, J., Vauhkonen, M.: Simulations of the heterogeneity of environments by finite element methods. Math. Comput. Simul. 39, 155-172 (1995)
    • (1995) Math. Comput. Simul. , vol.39 , pp. 155-172
    • Kaipio, J.P.1    Tervo, J.2    Vauhkonen, M.3
  • 37
    • 0013001564 scopus 로고
    • On the isoperimetric nature of a rearrangement inequality and its consequences for some variational problems
    • Kawohl, B.: On the isoperimetric nature of a rearrangement inequality and its consequences for some variational problems. Arch. Ration. Mech. Anal. 94, 227-243 (1986)
    • (1986) Arch. Ration. Mech. Anal. , vol.94 , pp. 227-243
    • Kawohl, B.1
  • 38
    • 0346338087 scopus 로고    scopus 로고
    • Modeling biological invasion into periodically fragmented environments
    • Kinezaki, N., Kawasaki, K., Takasu, F., Shigesada, N.: Modeling biological invasion into periodically fragmented environments. Theor. Population Biol. 64, 291-302 (2003)
    • (2003) Theor. Population Biol. , vol.64 , pp. 291-302
    • Kinezaki, N.1    Kawasaki, K.2    Takasu, F.3    Shigesada, N.4
  • 41
    • 0021015495 scopus 로고
    • Minimum domains for spatial patterns in a class of reaction-diffusion equations
    • Murray, J.D., Sperb, R.P.: Minimum domains for spatial patterns in a class of reaction-diffusion equations. J. Math. Biol. 18, 169-184 (1983)
    • (1983) J. Math. Biol. , vol.18 , pp. 169-184
    • Murray, J.D.1    Sperb, R.P.2
  • 42
    • 84989774895 scopus 로고    scopus 로고
    • Pinsky, R.G.: Positive harmonic functions and diffusion. Cambridge University Press, 1995
  • 43
    • 0040970045 scopus 로고
    • Second order elliptic operators with periodic coefficients: Criticality theory, perturbations, and positive harmonic functions
    • Pinsky, R.G.: Second order elliptic operators with periodic coefficients: criticality theory, perturbations, and positive harmonic functions. J. Funct. Anal. 129, 80-107 (1995)
    • (1995) J. Funct. Anal. , vol.129 , pp. 80-107
    • Pinsky, R.G.1
  • 44
    • 0030486030 scopus 로고    scopus 로고
    • Transience, recurrence and local extinction properties of the support for supercritical finite measure-valued diffusions
    • Pinsky, R.G.: Transience, recurrence and local extinction properties of the support for supercritical finite measure-valued diffusions. Ann. Probab. 24, 237-267 (1996)
    • (1996) Ann. Probab. , vol.24 , pp. 237-267
    • Pinsky, R.G.1
  • 45
    • 33746815700 scopus 로고
    • On a nonlinear elliptic eigenvalue problem with Neumann boundary conditions, with an application to population genetics
    • Senn, S.: On a nonlinear elliptic eigenvalue problem with Neumann boundary conditions, with an application to population genetics. Commun. Part. Diff. Equations 8, 1199-1228 (1983)
    • (1983) Commun. Part. Diff. Equations , vol.8 , pp. 1199-1228
    • Senn, S.1
  • 46
    • 0000076428 scopus 로고
    • On positive solutions of a linear elliptic eigenvalue problem with Neumann boundary conditions
    • Senn, S., Hess, P.: On positive solutions of a linear elliptic eigenvalue problem with Neumann boundary conditions. Math. Ann. 258, 459-470 (1981/82)
    • (1981) Math. Ann. , vol.258 , pp. 459-470
    • Senn, S.1    Hess, P.2
  • 47
    • 84989772282 scopus 로고    scopus 로고
    • Shigesada, N., Kawasaki, K.: Biological invasions: theory and practice. Oxford Series in Ecology and Evolution, Oxford : Oxford University Press, 1997
  • 48
  • 49
    • 0009636209 scopus 로고
    • Random dispersal in theoretical populations
    • Skellam, J.G.: Random dispersal in theoretical populations. Biometrika 38, 196-218 (1951)
    • (1951) Biometrika , vol.38 , pp. 196-218
    • Skellam, J.G.1
  • 50
    • 0348143251 scopus 로고    scopus 로고
    • On spreading speed and travelling waves for growth and migration models in a periodic habitat
    • Weinberger, H.: On spreading speed and travelling waves for growth and migration models in a periodic habitat. J. Math. Biol. 45, 511-548 (2002)
    • (2002) J. Math. Biol. , vol.45 , pp. 511-548
    • Weinberger, H.1
  • 51
    • 21144464889 scopus 로고
    • Existence of planar flame fronts in convective-diffusive periodic media
    • Xin, X.: Existence of planar flame fronts in convective-diffusive periodic media. Arch. Ration. Mech. Anal. 121, 205-233 (1992)
    • (1992) Arch. Ration. Mech. Anal. , vol.121 , pp. 205-233
    • Xin, X.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.