Contact information

arnaud.ducrot@u-bordeaux.fr

Université de Bordeaux
Institut de Mathématiques de Bordeaux UMR 5251
351, cours de la Libération
F 33 405 TALENCE



Publications

  1. A. Ducrot and J.-S. Guo, Asymptotic behaviour of solutions to a class of diffusive predator-prey systems, Journal of Evolution Equations, to appear.
  2. M. Alfaro, A. Ducrot and T. Giletti, Travelling waves for a non-monotone bistable equation with delay: existence and oscillations, Proceedings of the London Mathematical Society, to appear.
  3. A. Ducrot, J.-S. Guo and M. Shimojo, Behaviors of solutions for a singular prey-predator model and its shadow system, Journal of Dynamics and Differential Equations, to appear.
  4. J.-B. Burie, A. Ducrot and A.A. Mbengue, Asymptotic behaviour of an age and infection age structured model for the propagation of fungal diseases in plants, Discrete Contin. Dyn. Syst. Ser. B 22 (2017), 2879–2905.
  5. R. Djidjou-Demasse, A. Ducrot and F. Fabre, Steady state concentration for a phenotypic structured problem modelling the evolutionary epidemiology of spore producing pathogens, Mathematical Models and Methods in Applied Sciences, 27 (2017), 385–426. PDF
  6. A. Ducrot, P. Magal and O. Seydi, Singular perturbation for an abstract non-densely defined Cauchy problem, Journal of Evolution Equations, 17 (2017), 1089–1128. PDF
  7. A. Ducrot, Spatial propagation for a two component reaction-diffusion system arising in population dynamics, Journal of Differential Equations, 260 (2016), 8316–8357. PDF
  8. A. Ducrot and H. Matano, Plant disease propagation in a striped periodic medium. Applied analysis in biological and physical sciences, 121–164, Springer Proc. Math. Stat., 186, Springer, New Delhi, 2016.
  9. A. Ducrot, A multi-dimensional bistable nonlinear diffusion equation in a periodic medium, Mathematische Annalen, 366 (2016), 783–818. PDF
  10. A. Ducrot, P. Magal and O. Seydi, Persistence of exponential trichotomy for linear operators: A Lyapunov-Perron approach , Journal of Dynamics and Differential Equations, 28 (2016), 93–126. PDF
  11. A. Ducrot, On the large time behaviour of the multi-dimensional Fisher-KPP equation with compactly supported initial data, Nonlinearity, 28 (2015), 1043--1076. PDF
  12. C. Benosman, B. Ainseba and A. Ducrot, Optimization of Cytostatic Leukemia Therapy in an Advection–Reaction–Diffusion Model, Journal of Optimization Theory and Applications, 167 (2015), 296--325.
  13. J.B. Burie and A. Ducrot, A field scale model for the spread of fungal diseases in crops: the example of a powdery mildew epidemic over a large vineyard, Mathematical Methods in the Applied Sciences, 38 (2015), 3720-3737.
  14. A. Ducrot, P. Magal and O. Seydi, A finite-time condition for exponential trichotomy in infinite dynamical systems, Canadian Journal Math., 38 (2015), 3720-3737.
  15. P. Zongo, A. Ducrot, J.-B. Burie and C. Beaumont, Prevalence of Salmonella in flocks housed in enriched cages, Epidemiology and Infection, 38 (2015), 3720--3737.
  16. A. Ducrot and P. Magal, Asymptotic behaviour of a non-local diffusive logistic equation , SIAM Journal on Mathematical Analysis, 46 (2014), 1731-1753. PDF
  17. A. Ducrot and G. Nadin, Asymptotic behaviour of travelling waves for the delayed Fisher-KPP equation , Journal of Differential Equations, 256 (2014), 3115-3140. PDF
  18. A. Ducrot, P. Magal and O. Seydi, A singularly perturbed Delay Differential Equation modeling nosocomial infections, Differential and Integral Equations, to appear. PDF
  19. A. Ducrot and T. Giletti, Convergence to a pulsating travelling wave for an epidemic reaction-diffusion system with non-diffusive susceptible population, Journal of Mathematical Biology, 69 (2014), 533-552. PDF
  20. M. Alfaro and A. Ducrot, Propagating interface in a monostable reaction-diffusion equation with time delay , Differential and Integral Equations, 27 (2014), 81-104. PDF
  21. A. Ducrot and M. Langlais, Global weak solution for a singular two component reaction-diffusion system, Bulletin of the London Mathematical Society, 46 (2014), 1--13. PDF
  22. A. Ducrot, T. Giletti and H. Matano, Existence and convergence to a propagating terrace in one-dimensional reaction-diffusion equations, Trans. A.M.S., 366 (2014), 5541--5566. PDF
  23. R.D. Demasse and A. Ducrot, An age-structured within-host model for multi-strain malaria infections, SIAM Journal on Applied Mathematics, 73 (2013), 572--593. PDF
  24. A. Ducrot, Convergence to generalized transition waves for some Holling-Tanner prey- predator reaction-diffusion system, Journal de Mathématiques Pures et Appliquées, 100 (2013), 1--15. PDF
  25. A. Ducrot and S. Madec, Singularly perturbed elliptic system modelling the competitive interactions for a single resource, Mathematical Models and Methods in Applied Sciences, 23 (2013), 1939-1977. PDF
  26. C. Beaumont, J.B. Burie, A. Ducrot and P. Zongo, Propagation of Salmonella within an industrial hens house, SIAM Journal on Applied Mathematics, 72 (2012), 1113--1148. PDF
  27. A. Ducrot, M. Langlais and P. Magal, Multiple travelling waves for an SI-epidemic models, Networks and Heterogeneous Media, 8 (2013), 171--190.
  28. A. Ducrot and J.-S. Guo, Quenching behaviour for a singular predator-prey model, Nonlinearity 25 (2012), 2059--2073. PDF
  29. A. Ducrot and M. Langlais, A singular reaction-diffusion system modelling predator-prey interactions: invasion and co-extinction waves, Journal of Differential Equations 253 (2012), 502--532. PDF
  30. H. d’Albis, E. Augeraud-Véron, E. Djemai and A. Ducrot, The Dispersion of Age Difeferences between Partners and the Asymptotic Dynamics of the HIV Epidemic, Journal of Biological Dynamics, 6 (2012), 695--717.
  31. A. Ducrot, P. Magal and S. Ruan, Projectors on the generalized eigenspaces for partial differential equations with delay, in ``Infinite Dimensional Dynamical Systems'', J. Mallet-Paret, J. Wu, Y. Yi, and H. Zhu (eds.), Fields Institute Communications Vol. 64, 353-390. PDF
  32. A. Ducrot, M. Langlais and P. Magal, Qualitative analysis and travelling wave solutions for the SI model with vertical transmission, Communication in Pure and Applied Analysis, 11 (2012), 97--113. PDF
  33. A. Ducrot and P. Magal, Travelling wave solution for infection-age structured model with vital dynamics, Nonlinearity 24 (2011), 2891--2911. PDF
  34. J. Arino, A. Ducrot and P. Zongo, A metapopulation model for malaria with transmission-blocking partial immunity in hosts, Journal of Mathematical Biology 64 (2012), 423--448. PDF
  35. M. Alfaro and A. Ducrot, Sharp Interface limit of the Fisher-KPP equation, Communication in Pure and Applied Analysis 11 (2012), 1--18. PDF
  36. A. Ducrot, F. Le Foll, P. Magal, H. Murakawa, J. Pasquier and G. F. Webb, An in vitro cell population dynamics model incorporating cell size, quiescence, and contact inhibition, Mathematical Models and Methods in Applied Sciences 21 (2011), Suppl. 871--892. PDF
  37. A. Ducrot, P. Magal and O. Seydi, Nonlinear boundary conditions derived by singular perturbation in age structured population dynamics model, Journal of Applied Analysis and Computation, 1 (2011), 373--395. PDF
  38. M. Alfaro and A. Ducrot, Sharp interface limit of the Fisher-KPP equation when initial data have slow exponential decay, DCDS B, 16 (2011), 15--29. PDF
  39. A. Ducrot, M. Marion and V. Volpert, Spectrum of some integro-differential operators and stability of travelling waves, Nonlinear Analysis T.M.A., 74 (2011), 4455--4473. PDF
  40. A. Ducrot, Travelling waves for a size and space structured model in population dynamics: Point to sustained oscillating solution connections, Journal of Differential Equations, 250 (2011), 410--449. PDF
  41. A. Ducrot, V. Guyonne and M. Langlais, Some remarks on the qualitative properties of solutions to a predator-prey model posed on non coincident spatial domains, DCDS S, 4 (2011), 67--82.
  42. I. Demin, A. Ducrot and V. Volpert, Spatial distribution of cell populations in the process of erythropoiesis, IEJPAM, 01 (2010), 143--161. PDF
  43. A. Ducrot, P. Magal and S. Ruan, Une introduction aux modèles de dynamique de populations structurées en âges et aux problèmes de bifurcations, Gazette des mathématiciens, 125 (2010), 27--40. PDF
  44. A. Ducrot, P. Magal and S. Ruan, Travelling wave solutions in multi-group age-structured epidemic models , Arch. Rational Mech. Anal., 195 (2010), 311--331. PDF
  45. A. Ducrot, Z. Liu and P. Magal, Projectors on the generalized eigenspaces for neutral functional differential equations in Lp spaces, Canadian Journal of Mathematics, 62 (2010), 74--93. PDF
  46. A. Ducrot, K. Prevost and P. Magal, Integrated semigroup and parabolic equation: Part I, linear perturbation of almost sectorial operators, Journal of Evolution Equations, 10 (2010), 263--291. PDF
  47. A. Bonneu, T. Fourcaud, A. Ducrot and M. Langlais, Proposition of a conceptual density based model to describe fine root networks in tree root systems. Proc. of the Third International Symposium on Plant Growth Modeling, Simulation, Visualization and Applications, Li, B., Guo, Y., Jaeger, M. (Eds). Los Alamitos : IEEE Computer Society (2010), pp. 18--25.
  48. J.B. Burie and A. Ducrot, Travelling waves solution for some models in phytopathology, Nonlinear Analysis RWA 10 (2009), pp. 2307-2325.
  49. A. Ducrot and P. Magal, Travelling wave solutions for an infection-age stuctured model with diffusion, Proc. Roy. Soc. Edimburg. A 139 (2009), 459--482. PDF
  50. N. Apreutesei, A. Ducrot and V. Volpert, Travelling Waves for Integro-differential Equations, DCDS B, 11 (2009), 541--561.
  51. M. Adimy, A. Ducrot and C. Kou, On the dynamics of an impulsive model of hematopoiesis, Math. Mod. Natural Phenomena, 4 (2009), 68--91. PDF
  52. A. Ducrot, S.B. Sirima, B. Somé and P. Zongo, A mathematical model for malaria involving differential susceptibility, exposedness and infectivity of human host, Journal of Biological Dynamics, 3 (2009), 574--598. PDF
  53. J. Chu, A. Ducrot, P. Magal and S. Ruan, Hopf bifurcation for a size structured population dynamics model with random growth, Journal of Differential Equations, 247 (2009), 956--1000. PDF
  54. P. Auger and A. Ducrot, A model of fishery with fish stock involving delay equations, Phi. Trans. Roy. Soc. A 367 (2009), 4907--4922.
  55. A. Ducrot, Z. Liu and P. Magal, Essential growth rate for bounded linear perturbation of non-densely defined Cauchy problems, J. Math. Anal. Appl. 341, pp. 501-518 (2008).
  56. A. Ducrot and M. Langlais, Travelling waves in invasion processes with pathogens, Mathematical Models and Methods in Applied Sciences, 18 (2008), 325--349.
  57. A. Ducrot, M. Marion and V. Volpert, Reaction-diffusion problems with non Fredholm operators, Adv. Diff. Equations, 13 (2008), 1151-1192.
  58. N. Apreutesei, A. Ducrot and V. Volpert, Competition of species with intra-specific competition, Math. Modelling of Natural Phenomena, 3 (2008), 1-27.
  59. A. Ducrot, M. Marion, V. Volpert. Reaction-diffusion waves (with the Lewis number different from 1). Publibook, Paris (2008).
  60. A. Ducrot, Travelling wave solutions for a scalar age-structured equation, DCDS B, 7 (2007), 251--273.
  61. A. Ducrot and V. Volpert, On a model of leukemia development with a spatial cell distribution, Math. Modelling of Natural Phenomena, 2 (2007), 101--120.
  62. K. Allali, A. Ducrot, A. Taik and V. Volpert, Convective instability of reaction fronts in porous media, Math. Modelling of Natural Phenomena, 2 (2007), 20--39.
  63. A. Ducrot, Structural Stability of Combustion Models with complex chemistry, Mathematical Models and Methods in Applied Sciences, 16 (2006), 793--817.
  64. A. Ducrot, M. Marion and V. Volpert, Reaction-diffusion-convection systems with non Fredholm operators, Int. J. Pure Appl. Math, 27 (2006), 179--204.
  65. A. Ducrot, Multi-dimensional combustion waves for Lewis number close to one, Mathematical Methods in the Applied Sciences, 30 (2006), 291--304.
  66. J.B. Burie, A. Calonnec and A. Ducrot, Singular perturbation analysis of travelling waves for a model in phytopathology, Math. Modelling of Natural Phenomena, 01 (2006), 49--63.
  67. N. Bessonov, A. Ducrot and V. Volpert, Modelling of Leukemia development in the bone marrow, Proc. of the annual Symposium on "Mathematics applied in Biology and Biophysics", Tome XLVIII, vol.2 (2005), 79--88.
  68. S. Bidali, A. Ducrot, A. Mariani and M. Rustici, Self-ignition of Polymerization fronts with convection : the "Rainstorm Effect", e-Polymers, 44 (2005).
  69. A. Ducrot and V. Volpert, Modelling of convective heat explosion, Journal of Technical Physics, 46 (2005), 129--143.
  70. A. Ducrot, M. Marion and V. Volpert, Systèmes de Réaction-Diffusion sans Propriété de Fredholm, CRAS, 340 (2005), 659--664.
  71. A. Ducrot and M. Marion, Two-dimensional travelling wave solutions of a system modeling near-equi-diffusional flames, Nonlinear Analysis, TMA, 61 (2005), 1105--1134. PDF