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Volumn 205, Issue 1, 2007, Pages 137-161

Adaptive dynamics via Hamilton-Jacobi approach and entropy methods for a juvenile-adult model

Author keywords

Adaptive dynamics; Constrained Hamilton Jacobi equation; Selection mutation process

Indexed keywords

ASYMPTOTIC STABILITY; COMPUTER SIMULATION; ENTROPY; MATHEMATICAL MODELS;

EID: 33845228647     PISSN: 00255564     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mbs.2006.09.012     Document Type: Article
Times cited : (22)

References (28)
  • 1
    • 0031272189 scopus 로고    scopus 로고
    • Necessary and sufficient conditions for asynchronous exponential growth in age structured cell population with quiescence
    • Arino O., Sánchez E., and Webb G.F. Necessary and sufficient conditions for asynchronous exponential growth in age structured cell population with quiescence. J. Math. Anal. Appl. 215 (1997) 499
    • (1997) J. Math. Anal. Appl. , vol.215 , pp. 499
    • Arino, O.1    Sánchez, E.2    Webb, G.F.3
  • 2
    • 0001087942 scopus 로고
    • Wavefront propagation for reaction diffusion systems of PDE
    • Barles G., Evans L.C., and Souganidis P.E. Wavefront propagation for reaction diffusion systems of PDE. Duke Math. J. 61 (1990) 835
    • (1990) Duke Math. J. , vol.61 , pp. 835
    • Barles, G.1    Evans, L.C.2    Souganidis, P.E.3
  • 3
    • 33845224635 scopus 로고    scopus 로고
    • G. Barles, B. Perthame B, Concentrations and constrained Hamilton-Jacobi equations arising in adaptive dynamics, Math. Contemp., (in preparation).
  • 5
    • 0034714170 scopus 로고    scopus 로고
    • A model for the adaptive dynamics of the maturation age
    • Calsina A., and Cuadrado S. A model for the adaptive dynamics of the maturation age. Ecol. Model. 133 (2000) 33
    • (2000) Ecol. Model. , vol.133 , pp. 33
    • Calsina, A.1    Cuadrado, S.2
  • 6
    • 16544394080 scopus 로고    scopus 로고
    • Small mutation rate and evolutionarily stable strategies in infinite dimensional adaptive dynamics
    • Calsina A., and Cuadrado S. Small mutation rate and evolutionarily stable strategies in infinite dimensional adaptive dynamics. J. Math. Biol. 48 (2004) 135
    • (2004) J. Math. Biol. , vol.48 , pp. 135
    • Calsina, A.1    Cuadrado, S.2
  • 7
    • 21644456015 scopus 로고    scopus 로고
    • Stationary solutions of a selection mutation model: the pure mutation case
    • Calsina A., and Cuadrado S. Stationary solutions of a selection mutation model: the pure mutation case. Math. Mod. Meth. Appl. Sci. 15 7 (2005) 1091
    • (2005) Math. Mod. Meth. Appl. Sci. , vol.15 , Issue.7 , pp. 1091
    • Calsina, A.1    Cuadrado, S.2
  • 8
    • 33845221517 scopus 로고    scopus 로고
    • À. Calsina, S. Cuadrado, Dinámica de poblaciones estructuradas y evolución fenoti{dotless}́pica, Bol. Soc. Esp. Mat. Appl. (in press).
  • 10
    • 0038695682 scopus 로고
    • Non-local reaction-diffusion equations modelling predator-prey coevolution
    • Calsina A., Perelló C., and Saldaña J. Non-local reaction-diffusion equations modelling predator-prey coevolution. Publ. Mat. 38 (1994) 315
    • (1994) Publ. Mat. , vol.38 , pp. 315
    • Calsina, A.1    Perelló, C.2    Saldaña, J.3
  • 11
    • 33845226261 scopus 로고    scopus 로고
    • S. Cuadrado, Adaptive dynamics in an infinite dimensional setting, PhD thesis, UAB, 2003.
  • 12
    • 84967708673 scopus 로고
    • User's guide to viscosity solutions of second order partial differential equations
    • Crandall M.G., and Lions P.-L. User's guide to viscosity solutions of second order partial differential equations. Bull. Amer. Math. Soc. 27 (1992) 1
    • (1992) Bull. Amer. Math. Soc. , vol.27 , pp. 1
    • Crandall, M.G.1    Lions, P.-L.2
  • 13
    • 0029693807 scopus 로고    scopus 로고
    • The dynamical theory of coevolution: a derivation from a stochastic ecological processes
    • Dieckmann U., and Law R. The dynamical theory of coevolution: a derivation from a stochastic ecological processes. J. Math. Biol. 34 (1996) 579
    • (1996) J. Math. Biol. , vol.34 , pp. 579
    • Dieckmann, U.1    Law, R.2
  • 14
    • 33845199960 scopus 로고    scopus 로고
    • O. Diekmann, Beginner's guide to adaptive dynamics, Banach Center Publications, vol. 63, 2004, pp. 47.
  • 15
    • 18844400055 scopus 로고    scopus 로고
    • The dynamics of adaptation: an illuminating example and a Hamilton-Jacobi approach
    • Diekmann O., Jabin P.-E., Mischler S., and Perthame B. The dynamics of adaptation: an illuminating example and a Hamilton-Jacobi approach. Theor. Popul. Biol. 67 4 (2005) 257
    • (2005) Theor. Popul. Biol. , vol.67 , Issue.4 , pp. 257
    • Diekmann, O.1    Jabin, P.-E.2    Mischler, S.3    Perthame, B.4
  • 16
    • 0002627660 scopus 로고
    • Global solutions of Boltzmann's equation and entropy inequality
    • DiPerna R.J., and Lions P.-L. Global solutions of Boltzmann's equation and entropy inequality. Arch. Rat. Mech. Anal. 114 (1991) 47
    • (1991) Arch. Rat. Mech. Anal. , vol.114 , pp. 47
    • DiPerna, R.J.1    Lions, P.-L.2
  • 17
    • 33845230981 scopus 로고    scopus 로고
    • M. Escobedo, S. Mischler, Qualitative properties of some Boltzmann like equations which do not fulfill a detailed balance condition, J.L. Vázquez, X. Cabré, J.A. Carrillo (Eds.), Recent Trends in Partial Differential Equations, Contemporary Mathematics, vol. 409, American Mathematical Society 2006.
  • 18
    • 33845205628 scopus 로고    scopus 로고
    • R. Ferriere, S. Méléard, N. Fournier, N. Champagnat, The mathematical of Darwinian evolution: from stochastic individual processes to adaptative dynamics, preprint (2004).
  • 19
    • 33845221328 scopus 로고    scopus 로고
    • G. Greiner, A typical Perron-Frobenius theorem with applications to an age-dependent population equation, in: F. Kappeld, W. Schapacher (Eds.), Lecture Notes in Math., Infinite Dimensional Systems, vol. 1076, 1983.
  • 20
    • 0031886729 scopus 로고    scopus 로고
    • Evolutionary singular strategies and the adaptive growth and branching of the evolutionary tree
    • Geritz S.A.H., Kisdi E., Meszena G., and Metz J.A.J. Evolutionary singular strategies and the adaptive growth and branching of the evolutionary tree. Evol. Ecol. 12 (1998) 35
    • (1998) Evol. Ecol. , vol.12 , pp. 35
    • Geritz, S.A.H.1    Kisdi, E.2    Meszena, G.3    Metz, J.A.J.4
  • 21
    • 33845197794 scopus 로고    scopus 로고
    • T. Kato, Perturbation theory for Linear Operators. Die Grundlehren der mathematischen Wissenschaften, Band 132, Springer-Verlag, New York, 1966.
  • 22
    • 34548719708 scopus 로고
    • The logic of animal conflict
    • Maynard-Smith J., and Price G.R. The logic of animal conflict. Nature 246 (1973) 15
    • (1973) Nature , vol.246 , pp. 15
    • Maynard-Smith, J.1    Price, G.R.2
  • 23
    • 33845200910 scopus 로고    scopus 로고
    • J.A.J. Metz, S.A.H. Geritz, G. Meszéna, F.J.A. Jacobs, J.S. van Heerwaarden, Adaptive dynamics, a geometrical study of the consequences of nearly faithful reproduction. Stochastic and spatial structures of dynamical systems (Amsterdam, 1995), pp. 183-231, Konink. Nederl. Akad. Wetensch. Verh. Afd. Natuurk. Eerste Reeks, 45, North-Holland, Amsterdam, 1996.
  • 24
    • 33845220835 scopus 로고    scopus 로고
    • P. Michel, General relative entropy in a nonlinear McKendrick model. M3AS (in press).
  • 25
    • 24044522878 scopus 로고    scopus 로고
    • P. Michel, S. Mischler, B. Perthame, General relative entropy inequality: an illustration on growth models, J. Math. Pure Appl. 84 (9) (2005) 1235.
  • 27
    • 0003316678 scopus 로고
    • Semigroups of linear operators and applications to partial differential equations
    • Springer, New York
    • Pazy A. Semigroups of linear operators and applications to partial differential equations. Appl. Math. Sci. vol. 44 (1983), Springer, New York
    • (1983) Appl. Math. Sci. , vol.44
    • Pazy, A.1
  • 28
    • 33845224399 scopus 로고    scopus 로고
    • H.H. Schaefer, Banach Lattices and Positive Operators. Die Grundlehren der mathematischen Wissenschaften, Band 215, Springer-Verlag, New York, Heidelberg, 1974.


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.