Existence of nontrivial steady states for populations structured with respect to space and a continuous trait

Communications on Pure and Applied Analysis

Volumn 11, Issue 1, 2012, Pages 83-96

  Arnold, Anton ^a   Desvillettes, Laurent ^b   Prévost, Céline ^c  

^a VIENNA UNIVERSITY OF TECHNOLOGY   (Austria)

^b UNIVERSITÉ PARIS SACLAY   (France)

^c UNIVERSITÉ D'ORLÉANS   (France)

Author keywords

Infnite dimensional reaction diffusion equations; Selection mutation competition migration models; Structured populations

Indexed keywords

EID: 82255169708     PISSN: 15340392     EISSN: 15535258     Source Type: Journal    
DOI: 10.3934/cpaa.2012.11.83     Document Type: Conference Paper

References (14)

1. H. Brezis, "Analyse Fonctionnelle," Masson, Paris, 1987.
2. F. Brezzi and G. Gilardi, "Fundamentals of P.D.E. for Numerical Analysis," preprint n. 446 of Istituto di Analisi Numerica, Pavia, 1984.
3. A. Calsinaand S. Cuadrado, Asymptotic stability of equilibria of selection-mutation equations, J. Math. Biol., 54 (2007), 489-511. (Pubitemid 46446803)
4. J. Carrillo, L. Desvillettes and K. Fellner, Exponential decay towards equilibrium for the inhomogeneous Aizenman-Bak model, Commun. Math. Phys., 278 (2008), 433-451.
5. J. Carrillo, L. Desvillettes and K. Fellner, Fast-reaction limit for the inhomogeneous Aizenman-Bak model, Kinetic and Related Models, 1 (2008), 127-137.
6. R. Dautray and J.-L. Lions, "Mathematical Analysis and Numerical Methods for Science and Technology," vol 1. Physical Origins and Classical Methods, Springer-Verlag, Berlin- Heidelberg-New York, 1990.
7. L. Desvillettes, R. Ferrìeres and C. Pŕevost, "Infinite Dimensional Reaction-Diffusion for Population Dynamics," preprint n. 2003-04 du CMLA, ENS de Cachan.
8. L. Desvillettes, P.-E. Jabin, S. Mischler and G. Raoul, On mutation-selection dynamics, Commun. Math. Sc., 6 (2008), 729-747.
9. O. Diekmann, P.-E. Jabin, S. Mischler and B. Perthame, The dynamics of adaptation: An illuminating example and a Hamilton-Jacobi approach, Theor. Popul. Biol., 67 (2005), 257-271. (Pubitemid 40678713)
10. P. Laureņcot and S. Mischler, Global existence for the discrete diffusive coagulation- fragmentation equations in L1, Rev. Mat. Iberoamericana, 18 (2002), 731-745. (Pubitemid 36224500)
11. P. Laureņcot and S. Mischler, The continuous coagulation- fragmentation equations with diffusion, Arch. Rational Mech. Anal., 162 (2002), 45-99. (Pubitemid 36185874)
12. G. Raoul, Local stability of evolutionary attractors for continuous structured populations, to appear in Monatshefte für Mathematik, 2011.
13. F. Rothe, "Global Solutions of Reaction-Diffusion Systems," Lecture Notes in Mathematics, vol. 1072. Springer-Verlag, Berlin-Heidelberg-New York-Tokyo, 1984.
14. J. Smoller, "Shock Waves and Reaction-Diffusion Equations," Second edition, Grundlehren der Mathematischen Wissenschaften, vol. 258. Springer-Verlag, New York, 1994.